Geospatial Fundamentals in R, Part 3: Raster Data
Patty Frontiera and Drew Hart, UC Berkeley D-Lab
Dec 2021
Part III Prep
This workshop assumes you have R and RSTudio installed on your computer.
Open the repo at https://github.com/dlab-berkeley/R-Geospatial-Fundamentals
- Download and unzip the zip file
- Take note of where the folder is located
Locate the file
Geospatial-Fundamentals-in-R-with-sf.Rprojin the folder and double-click on it. This will launch RStudio and with yourworking directoryset to the folder containing these workshop files.Check out the list of workshop files in the RSTUDIO
files panelin the bottom-right of the RStudio interface. Navigate to thedocsfolder to see the tutorial docs. Double-click on09_Raster_Data.Rmdto open that file in RStudio.Install the required libraries in RStudio, if you do not have them already
our_packages<- c("ggplot2", "sf", "tmap", "raster")
for (i in our_packages) {
if ( i %in% rownames(installed.packages()) == FALSE) {
install.packages(i)
}
}Part III Overview
Introductions: me, you, the D-Lab, the workshop series
Review basic raster concepts
Read in some vector data and new raster data
Make some raster and combined raster-vector maps
Run some raster and raster-vector operations and analyses
R Packages for working with Geospatial Data
Old favorites
spfor vector datarasterfor raster data
The raster package depends on sp for vector-raster operations.
New packages:
sfnot so new anymore, the new default for vector dataterradepends on thesffor vector-raster operations.
See this nice chart from the online book Geocomputation with R https://geocompr.robinlovelace.net/figures/01-cranlogs.png
R Spatial Libraries
Let’s load the libraries we will use
library(sf) # simple features objects and methods
library(tmap) # mapping spatial objects
library(raster) # reading in and operating on rasters
library(here) # build paths from folder with .rproj fileSet your working directory
A common practice for any coding script is to set your working directory to point to the folder in which the files you will be working with reside. In R, you would use the command setwd to set your working directory to the location of the tutorial files.
For example:
my_folder = "~/Documents/repos/R-Geospatial-Fundamentals"
setwd(my_folder)Alternately, you can use the here() function from the here package to build file paths that start at the project directory, as defined by the location of the Rproj file. This method is the preferred way of setting the working directory in R and less error prone.
Load some files from Parts I and II
We are going to start by using the sf library to load some vector point and polygon data for San Francisco that we used in part 1 & 2 of this workshop.
SF Census Tracts
Read in the data from an ESRI shapefile to an sf spatial object with the function st_read.
# read the 'sftracts_wpop' shapefile
SFtracts_NAD83 <- st_read(here("notebook_data",
"part_3",
"sftracts_wpop.shp"))## Reading layer `sftracts_wpop' from data source
## `/Users/pattyf/Documents/Dlab/workshops/AY2022/Dev/notebook_data/part_3/sftracts_wpop.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 195 features and 10 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -122.5145 ymin: 37.70813 xmax: -122.328 ymax: 37.86334
## Geodetic CRS: NAD83# Take a look
head(SFtracts_NAD83)## Simple feature collection with 6 features and 10 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -122.4432 ymin: 37.77376 xmax: -122.4055 ymax: 37.80218
## Geodetic CRS: NAD83
## STATEFP COUNTYFP TRACTCE AFFGEOID GEOID NAME LSAD ALAND
## 1 06 075 010700 1400000US06075010700 06075010700 107 CT 183170
## 2 06 075 012201 1400000US06075012201 06075012201 122.01 CT 92048
## 3 06 075 013102 1400000US06075013102 06075013102 131.02 CT 237886
## 4 06 075 013500 1400000US06075013500 06075013500 135 CT 235184
## 5 06 075 015500 1400000US06075015500 06075015500 155 CT 311339
## 6 06 075 016300 1400000US06075016300 06075016300 163 CT 245867
## AWATER pop14 geometry
## 1 0 5311 MULTIPOLYGON (((-122.4129 3...
## 2 0 4576 MULTIPOLYGON (((-122.4183 3...
## 3 0 2692 MULTIPOLYGON (((-122.4302 3...
## 4 0 2592 MULTIPOLYGON (((-122.4362 3...
## 5 0 3918 MULTIPOLYGON (((-122.4432 3...
## 6 0 4748 MULTIPOLYGON (((-122.4332 3...Take a look at the CRS
Coordinate reference system details
# get CRS details
st_crs(SFtracts_NAD83)## Coordinate Reference System:
## User input: NAD83
## wkt:
## GEOGCRS["NAD83",
## DATUM["North American Datum 1983",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## CS[ellipsoidal,2],
## AXIS["latitude",north,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433]],
## AXIS["longitude",east,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433]],
## ID["EPSG",4269]]SF Properties 2015
Read in property point data from a CSV file.
# read from CSV file
SFhomes <- read.csv(here("notebook_data",
"part_3",
"sf_properties.csv"),
stringsAsFactors = FALSE)
# subset the data because it is too much
SFhomes15 <- subset(SFhomes, as.numeric(SalesYear) == 2015)
# convert it to an `sf` object
SFhomes15_WGS84 <- st_as_sf(SFhomes15,
coords = c('lon', 'lat'),
crs = 4326)Do the CRSs match?
#take a look at the CRS details
st_crs(SFhomes15_WGS84)## Coordinate Reference System:
## User input: EPSG:4326
## wkt:
## GEOGCRS["WGS 84",
## DATUM["World Geodetic System 1984",
## ELLIPSOID["WGS 84",6378137,298.257223563,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## CS[ellipsoidal,2],
## AXIS["geodetic latitude (Lat)",north,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433]],
## AXIS["geodetic longitude (Lon)",east,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433]],
## USAGE[
## SCOPE["Horizontal component of 3D system."],
## AREA["World."],
## BBOX[-90,-180,90,180]],
## ID["EPSG",4326]]# Or the shorter proj4string
st_crs(SFhomes15_WGS84)$proj4string## [1] "+proj=longlat +datum=WGS84 +no_defs"CRS transformation of sf Objects
We can use the sf::st_transform function to reproject the SFhomes15_WGS84 data to match that of the SFtracts_NAD83 or (vice versa).
- NOTE: We’re overwriting the previous SFhomes15_sf object here!
- This is fine to do if we want, but we should always beware.
# transform CRS and output a new object, overwriting old one
SFhomes15_NAD83 <- st_transform(SFhomes15_WGS84, st_crs(SFtracts_NAD83))
# Check projection equality
st_crs(SFhomes15_NAD83) == st_crs(SFtracts_NAD83)## [1] TRUEMake a quick plot of the two NAD83 sf spatial dataframes
plot(SFtracts_NAD83$geometry)
plot(SFhomes15_NAD83$geometry, add=T, col="red")
Challenge 1
In the code cell below - transform SFtracts_NAD83 to WGS84 and name it SFtracts_WGS84 - take a look at the CRS info in the new - Plot the WGS84 homes on top of the transformed SF tracts
# YOUR CODE HERE
# transform SFtracts_NAD83 to WGS84
# SFtracts_WGS84 <-
# Take a look at the crs
#Plot the WGS84 homes on top of the transformed SF tractsNAD27 vs NAD83 vs WGS84
WGS84 is a geographic CRS (lon/lat) optimized for the globe. It is the default!
NAD83 is a geographic CRS optimized for North America. It’s best for USA data.
NAD27 is old and inaccurate! Don’t use it.
# Make sure we have the tract data from previous challenge!
SFtracts_WGS84 <- st_transform(SFtracts_NAD83, st_crs(SFhomes15_WGS84))
SFtracts_NAD27 <- st_transform(SFtracts_NAD83, 4267)
plot(SFtracts_WGS84$geometry, border="black")
plot(SFtracts_NAD83$geometry, border="green", add=T)
plot(SFtracts_NAD27$geometry, border="red", add=T)
Section 1: Raster Data in R
Read in a Raster
Use the fabulous raster package to read in a DEM
# Reading in and plotting raster files
#read in a Bay Area DEM (Digital Elevation Model)
#(from http://www.webgis.com/terr_pages/CA/dem1/sanfrancisco.html)
DEM <- raster(here("notebook_data",
"part_3",
"san_francisco-e.DEM"))Plot it
Make a quick map of the data to check it out
#plot it
plot(DEM)
Explore the Structure
To see a summary of the structure and content of a RasterLayer object, we can just enter the object’s name.
DEM## class : RasterLayer
## dimensions : 1201, 1201, 1442401 (nrow, ncol, ncell)
## resolution : 0.0008333333, 0.0008333333 (x, y)
## extent : -123.0004, -121.9996, 36.99958, 38.00042 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=NAD27 +no_defs
## source : san_francisco-e.DEM
## names : san_francisco.e
## values : -32768, 32767 (min, max)You can view more detail in the RStudio Environment panel.
Explore the Structure
A raster should really just be a matrix of data, with metadata specifying it the correct location on the Earth’s surface, right?
In a raster object, the data and metadata will all be saved in their own ‘slots’, which are indexed by ‘@’ rather than ‘$’.
(‘Slots’ are components used to organize ‘S4’ objects. ‘S4’ is a data-type commonly used by third-party packages to define their own special data structures.)
Explore the Structure
Here’s some of the important metadata.
DEM@extent## class : Extent
## xmin : -123.0004
## xmax : -121.9996
## ymin : 36.99958
## ymax : 38.00042DEM@crs## CRS arguments: +proj=longlat +datum=NAD27 +no_defsDEM@ncols## [1] 1201DEM@nrows## [1] 1201dim(DEM)## [1] 1201 1201 1Explore the Structure
And notice that the DEM object is indeed an ‘S4’ object.
class(DEM)## [1] "RasterLayer"
## attr(,"package")
## [1] "raster"typeof(DEM)## [1] "S4"Explore the Structure
Note that a raster object’s structural organization and string-representation (the bit that is printed to the screen when you call the variable’s name) are fundamentally different from those of sf objects. We can explore that in the Environment panel.
Explore the Structure
For example, a RasterLayer has information on the resolution.
DEM## class : RasterLayer
## dimensions : 1201, 1201, 1442401 (nrow, ncol, ncell)
## resolution : 0.0008333333, 0.0008333333 (x, y)
## extent : -123.0004, -121.9996, 36.99958, 38.00042 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=NAD27 +no_defs
## source : san_francisco-e.DEM
## names : san_francisco.e
## values : -32768, 32767 (min, max)Explore the Structure
What does the resolution mean?
res(DEM)## [1] 0.0008333333 0.0008333333(DEM@extent@xmax - DEM@extent@xmin) / DEM@ncols## [1] 0.0008333333(DEM@extent@ymax - DEM@extent@ymin) / DEM@nrows## [1] 0.0008333333DEM## class : RasterLayer
## dimensions : 1201, 1201, 1442401 (nrow, ncol, ncell)
## resolution : 0.0008333333, 0.0008333333 (x, y)
## extent : -123.0004, -121.9996, 36.99958, 38.00042 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=NAD27 +no_defs
## source : san_francisco-e.DEM
## names : san_francisco.e
## values : -32768, 32767 (min, max)It’s the cell-size! That is, the real-world distance of the x and y sides of each cell (i.e. pixel) in our RasterLayer, expressed in the distance units of the object (as determined by its projection). What are those distance units?
A Note about Distance units
Are a component of the CRS.
If you want meters or feet you need to transform (or reproject) the raster to a projected 2D CRS that uses those units.
For example, UTM zone 10N, NAD83 (epsg code = 26911) is a widely used projected CRS for Northern CA spatial data analysis.
We will practice reprojecting rasters in just a little bit!
Explore the Structure
As for our matrix of data, it should live somewhere inside the @data slot, right?
str(DEM@data)## Formal class '.SingleLayerData' [package "raster"] with 13 slots
## ..@ values : logi(0)
## ..@ offset : num 0
## ..@ gain : num 1
## ..@ inmemory : logi FALSE
## ..@ fromdisk : logi TRUE
## ..@ isfactor : logi FALSE
## ..@ attributes: list()
## ..@ haveminmax: logi TRUE
## ..@ min : num -32768
## ..@ max : num 32767
## ..@ band : int 1
## ..@ unit : chr ""
## ..@ names : chr "san_francisco.e"Explore the Structure
There’s a bunch of stuff there. Let’s take a look at the @data@values slot…
DEM@data@values## logical(0)Explore the Structure
What happened there? How can our data be logical(0)? Where’s our data?
DEM@data@inmemory## [1] FALSEDEM@data@fromdisk## [1] TRUEIt appears our data was not all read into memory. Instead, our RasterLayer object contains a pointer to where that data is held on disk (to save computer memory).
Explore the Structure
How do we see the values, then?
Well, we can still subset the values, using two-dimensional bracket subsetting notation, just as we’d expect for a matrix.
DEM[1:4, 1:4] # return the values in rows 1-4 and cols 1-4## [1] 120 120 117 111 123 123 118 109 127 127 119 113 130 130 125 119DEM[1,4] # return the value in the cell at row 1, col 4##
## 111And we’ll get back a vector of the values from that subsetted matrix, unfolded.
Explore the Structure
We can even subset the entire thing, getting back all of the values.
DEM[,]## [1] 120 120 117 111 104 98 92 89 87 85 82 80 79 76 72 67 57 45
## [19] 32 20 12 6 3 1 0 0 0 0 0 0 0 0 0 0 0 0
## [37] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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## [91] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [109] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [127] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [145] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [163] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [181] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [199] 0 0 0 0 0 0 0 1 3 11 19 27 33 40 51 59 70 69
## [217] 91 108 123 140 158 168 185 196 204 205 204 194 195 186 172 164 152 135
## [235] 118 101 81 69 62 54 50 53 53 54 56 58 74 91 107 126 143 162
## [253] 174 202 223 234 246 260 282 308 336 367 383 385 379 371 359 345 325 311
## [271] 280 259 249 236 226 215 202 188 170 157 145 130 118 109 101 95 89 86
## [289] 83 81 82 79 79 85 90 96 99 100 103 111 119 122 123 124 125 128
## [307] 143 158 168 175 182 188 192 209 222 226 234 250 265 279 291 304 306 305
## [325] 326 344 355 367 379 389 395 395 391 380 371 365 352 329 314 300 281 271
## [343] 259 239 214 188 172 158 140 122 112 110 110 115 146 173 180 182 212 243
## [361] 263 275 282 265 249 218 202 198 191 189 194 194 196 193 192 198 216 231
## [379] 239 242 246 249 262 274 284 294 302 306 322 342 357 368 374 371 362 357
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## [973] 176 178 179 180 182 185 188 191 193 194 194 193 193 193 193 192 191 191
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## [ reached getOption("max.print") -- omitted 1342402 entries ]Explore the Structure
And we could even then turn that vector back into a matrix of the proper dimensions.
#coerce a subset of the data values to a matrix,
# with the appropriate number of rows and columns
matrix(DEM[1:4,1:4], ncol = 4, byrow = TRUE)## [,1] [,2] [,3] [,4]
## [1,] 120 120 117 111
## [2,] 123 123 118 109
## [3,] 127 127 119 113
## [4,] 130 130 125 119#coerce our whole raster data values to a matrix,
# with the appropriate number of rows and cols
matrix(DEM[,], ncol = ncol(DEM), byrow = TRUE)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
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## [2,] 101 103 111 119 123 125 124 123 122 141
## [3,] 102 105 111 119 126 129 126 123 122 141
## [4,] 103 106 111 118 125 128 127 124 122 127
## [5,] 105 108 112 116 120 124 124 123 122 125
## [6,] 107 110 113 116 118 121 122 122 121 127
## [7,] 110 111 114 117 119 121 121 121 121 128
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## [10,] 115 116 117 119 120 121 121 121 122 128
## [11,] 116 117 118 119 120 121 121 121 121 127
## [12,] 117 118 119 119 120 120 121 121 121 125
## [13,] 119 119 119 120 120 121 121 121 121 124
## [14,] 120 120 120 120 121 121 121 121 121 121
## [15,] 121 121 121 121 121 121 121 121 121 121
## [16,] 126 121 121 121 121 121 121 121 121 121
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## [20,] 175 167 159 154 146 138 130 121 121 121
## [21,] 188 178 170 168 160 151 143 134 123 121
## [22,] 209 198 182 182 174 165 156 146 133 121
## [23,] 234 231 215 201 188 178 169 157 143 131
## [24,] 260 255 243 227 208 192 182 168 153 139
## [25,] 292 291 267 243 227 208 188 179 163 147
## [26,] 304 304 304 257 243 227 200 182 172 155
## [27,] 304 297 267 251 246 232 203 185 173 155
## [28,] 288 277 246 244 225 212 182 186 169 156
## [29,] 299 295 274 244 232 214 203 190 178 173
## [30,] 312 308 304 253 243 225 217 210 205 194
## [31,] 320 311 305 243 239 233 228 226 224 218
## [32,] 329 317 296 275 254 242 242 253 255 246
## [33,] 342 323 304 289 274 272 275 284 292 263
## [34,] 359 339 320 304 296 295 299 306 303 293
## [35,] 368 358 343 331 304 304 320 313 307 304
## [36,] 375 374 373 372 365 353 339 319 307 290
## [37,] 384 393 396 391 365 365 365 318 291 263
## [38,] 392 411 425 412 365 358 330 309 277 245
## [39,] 387 402 426 405 365 341 320 304 262 243
## [40,] 371 380 389 396 371 339 304 306 281 260
## [41,] 365 365 367 369 365 353 331 304 302 304
## [42,] 365 365 365 366 366 365 347 324 304 305
## [43,] 365 365 365 365 365 365 365 352 328 314
## [44,] 365 365 365 365 365 365 365 365 365 341
## [45,] 365 365 364 364 365 365 365 365 365 365
## [46,] 365 365 364 364 364 365 365 365 365 365
## [47,] 365 360 360 361 363 365 365 365 365 365
## [48,] 365 350 352 356 359 363 365 365 365 365
## [49,] 365 337 340 347 354 362 365 365 365 365
## [50,] 365 314 323 335 348 365 364 365 365 365
## [51,] 326 303 301 312 327 343 365 365 364 365
## [52,] 319 296 282 293 304 323 347 363 359 361
## [53,] 317 291 264 276 291 304 324 341 352 357
## [54,] 315 279 247 251 267 283 298 318 336 344
## [55,] 315 291 243 246 243 262 283 307 320 330
## [56,] 312 298 243 244 244 243 262 290 308 317
## [57,] 303 261 266 247 244 243 243 274 292 304
## [58,] 308 269 243 246 243 240 243 261 276 285
## [59,] 307 284 243 238 232 228 236 248 259 264
## [60,] 305 274 242 226 211 198 216 238 245 246
## [61,] 304 304 243 210 182 188 182 213 243 243
## [62,] 304 304 243 214 182 182 184 193 223 243
## [63,] 290 304 243 219 182 182 182 182 192 189
## [64,] 275 296 263 243 182 182 182 182 182 182
## [65,] 254 259 243 226 195 182 182 182 182 182
## [66,] 243 246 248 243 218 199 182 182 182 182
## [67,] 245 247 249 247 237 212 182 182 182 182
## [68,] 248 252 257 259 257 243 215 182 182 182
## [69,] 253 261 269 278 291 272 256 211 182 182
## [70,] 253 263 273 285 304 304 304 233 182 182
## [71,] 238 249 261 272 284 297 304 270 230 198
## [72,] 217 228 243 255 267 276 274 254 252 243
## [73,] 203 207 225 243 255 260 259 247 245 246
## [74,] 185 183 193 213 227 228 233 237 244 243
## [75,] 182 182 178 182 189 182 200 214 231 243
## [76,] 170 162 159 163 166 163 176 190 206 223
## [77,] 126 121 130 134 132 121 150 170 182 203
## [78,] 107 113 118 123 118 119 127 154 182 187
## [79,] 85 93 103 103 106 109 115 131 154 182
## [80,] 67 76 86 89 92 96 101 113 120 133
## [81,] 42 60 71 76 80 83 87 100 113 121
## [82,] 10 32 47 64 66 68 69 86 102 115
## [83,] 0 0 0 23 38 44 53 67 85 97
## [,308] [,309] [,310] [,311] [,312] [,313] [,314] [,315] [,316] [,317]
## [1,] 158 168 175 182 188 192 209 222 226 234
## [2,] 157 168 176 183 190 195 210 223 232 238
## [3,] 156 166 175 183 189 195 210 223 232 238
## [4,] 141 157 170 179 185 193 206 218 228 236
## [5,] 136 150 165 176 182 189 199 211 221 231
## [6,] 138 151 163 174 180 185 193 203 213 220
## [7,] 138 150 161 171 178 182 189 196 203 208
## [8,] 138 148 159 169 177 182 186 189 192 196
## [9,] 139 149 159 170 177 181 183 184 185 186
## [10,] 138 149 159 169 177 181 182 182 182 182
## [11,] 137 147 158 169 176 180 182 182 182 182
## [12,] 137 146 157 169 178 181 182 182 182 182
## [13,] 136 147 159 174 182 181 182 182 182 182
## [14,] 127 140 156 175 181 182 182 182 182 182
## [15,] 121 121 139 158 182 182 182 182 182 182
## [16,] 121 121 121 131 157 172 176 180 181 182
## [17,] 121 121 121 131 141 155 171 178 180 181
## [18,] 121 121 121 121 127 146 171 180 182 182
## [19,] 121 121 121 121 121 134 182 180 182 182
## [20,] 121 121 121 121 121 121 155 182 182 182
## [21,] 121 121 121 121 121 121 129 154 174 182
## [22,] 121 121 121 121 121 121 121 133 153 168
## [23,] 124 121 121 121 121 121 121 121 137 150
## [24,] 132 126 121 121 121 121 121 121 121 133
## [25,] 138 130 125 122 121 121 121 121 121 121
## [26,] 144 133 127 124 121 121 121 121 121 121
## [27,] 141 126 125 123 122 121 121 121 121 121
## [28,] 140 121 121 122 121 121 121 121 121 121
## [29,] 154 131 121 121 121 121 121 121 121 121
## [30,] 182 155 121 121 121 121 121 121 121 121
## [31,] 197 182 144 121 121 121 121 121 121 121
## [32,] 229 182 162 134 121 121 121 121 121 121
## [33,] 243 223 182 163 144 121 121 121 121 121
## [34,] 269 243 220 191 172 135 121 121 121 121
## [35,] 304 261 243 204 188 162 121 121 121 121
## [36,] 269 253 226 192 177 153 121 121 121 121
## [37,] 243 209 182 188 173 149 134 121 121 121
## [38,] 226 199 186 182 179 156 138 124 121 121
## [39,] 243 228 205 185 175 160 141 121 124 122
## [40,] 250 243 216 182 176 157 144 121 121 122
## [41,] 275 243 231 212 187 167 158 150 139 128
## [42,] 304 243 243 239 225 182 179 182 182 161
## [43,] 304 264 243 251 242 227 207 228 208 190
## [44,] 323 304 288 276 271 263 243 246 243 215
## [45,] 354 328 312 301 299 305 294 274 254 243
## [46,] 365 347 333 332 335 320 308 304 271 254
## [47,] 365 360 354 359 362 340 318 304 281 260
## [48,] 365 365 365 364 365 345 324 304 281 259
## [49,] 365 365 365 365 365 346 325 304 274 250
## [50,] 365 365 365 365 365 348 325 304 263 243
## [51,] 365 365 365 365 365 353 324 304 243 235
## [52,] 364 365 365 365 365 351 312 299 259 238
## [53,] 365 365 365 365 365 344 322 304 280 265
## [54,] 352 361 365 365 365 359 327 309 298 283
## [55,] 339 348 356 365 365 365 327 315 309 304
## [56,] 326 335 343 351 358 335 320 313 309 307
## [57,] 313 322 330 337 342 326 316 311 308 307
## [58,] 296 309 317 321 329 321 315 311 309 307
## [59,] 267 285 304 304 316 318 315 312 309 308
## [60,] 241 254 268 279 302 310 310 310 309 307
## [61,] 223 221 243 243 275 304 306 306 306 306
## [62,] 202 182 207 230 254 290 304 305 305 305
## [63,] 184 186 183 193 235 277 304 304 304 304
## [64,] 182 183 182 205 231 272 304 304 304 304
## [65,] 182 182 182 208 241 265 280 297 304 304
## [66,] 182 182 192 205 232 254 266 279 290 304
## [67,] 182 182 182 189 214 241 249 261 268 282
## [68,] 182 182 182 182 199 243 242 243 243 259
## [69,] 182 182 182 182 199 213 223 215 225 235
## [70,] 182 182 182 182 182 186 182 182 199 216
## [71,] 182 182 182 181 179 180 181 182 182 192
## [72,] 213 182 182 180 173 175 178 181 182 204
## [73,] 243 213 182 179 168 170 175 182 189 207
## [74,] 244 243 228 171 137 151 163 177 188 213
## [75,] 243 243 211 167 121 121 142 163 182 198
## [76,] 229 216 203 167 121 121 121 147 172 182
## [77,] 201 199 195 167 121 121 121 142 182 185
## [78,] 190 190 188 169 130 121 121 121 145 170
## [79,] 182 184 184 173 143 121 121 121 121 140
## [80,] 165 182 182 177 155 137 121 121 121 121
## [81,] 142 163 182 182 169 145 131 121 121 121
## [82,] 127 142 153 170 168 149 133 123 121 119
## [83,] 109 121 121 139 138 134 130 121 117 117
## [,318] [,319] [,320] [,321] [,322] [,323] [,324] [,325] [,326] [,327]
## [1,] 250 265 279 291 304 306 305 326 344 355
## [2,] 251 266 279 291 304 307 306 327 344 355
## [3,] 251 266 279 291 304 304 308 327 342 353
## [4,] 245 257 270 277 285 291 304 310 327 346
## [5,] 240 249 256 263 267 273 284 293 305 321
## [6,] 229 237 243 249 252 256 267 276 288 302
## [7,] 215 223 232 237 241 244 254 264 277 290
## [8,] 201 210 221 231 237 242 248 260 278 292
## [9,] 190 200 214 227 237 242 247 261 282 294
## [10,] 185 195 211 227 237 242 246 257 271 284
## [11,] 185 195 211 227 236 242 244 250 261 271
## [12,] 182 190 200 217 233 243 243 241 245 258
## [13,] 182 182 182 198 205 216 228 234 239 243
## [14,] 182 182 182 182 182 191 216 225 234 240
## [15,] 182 182 182 182 182 202 210 220 231 238
## [16,] 182 182 182 182 185 196 207 215 228 239
## [17,] 182 182 182 182 188 195 203 212 229 243
## [18,] 182 182 182 182 188 194 200 204 223 242
## [19,] 182 182 182 182 182 184 186 182 203 234
## [20,] 182 182 182 182 182 182 182 183 182 215
## [21,] 182 182 181 180 181 182 182 182 192 210
## [22,] 182 176 173 176 179 181 182 182 188 206
## [23,] 155 155 164 170 177 181 182 182 186 198
## [24,] 135 139 153 164 174 180 182 182 182 185
## [25,] 121 124 143 161 179 182 182 182 182 182
## [26,] 121 121 121 153 182 182 182 182 182 182
## [27,] 121 121 121 129 149 169 179 182 182 182
## [28,] 121 121 121 121 121 141 162 182 182 177
## [29,] 121 121 121 121 121 121 148 166 177 174
## [30,] 121 121 121 121 121 121 127 148 157 167
## [31,] 121 121 121 121 121 121 121 131 144 157
## [32,] 121 121 121 121 121 121 121 121 130 146
## [33,] 121 121 121 121 121 121 121 121 121 137
## [34,] 121 121 121 121 121 121 121 121 122 134
## [35,] 121 121 121 121 121 121 121 121 121 129
## [36,] 121 121 121 121 121 121 121 121 121 121
## [37,] 121 121 121 121 121 121 121 121 121 121
## [38,] 121 121 121 121 121 121 121 121 121 121
## [39,] 121 121 121 121 121 121 121 121 121 121
## [40,] 122 121 121 121 121 121 121 121 121 121
## [41,] 122 121 121 121 121 121 121 121 121 121
## [42,] 139 121 121 121 121 121 121 121 121 121
## [43,] 172 138 121 121 121 121 121 121 121 121
## [44,] 182 162 137 121 121 121 121 121 121 121
## [45,] 218 184 160 142 127 121 121 121 121 121
## [46,] 243 211 182 160 141 121 121 121 121 121
## [47,] 245 223 187 177 160 136 121 121 121 121
## [48,] 249 224 189 185 182 143 130 121 121 121
## [49,] 234 201 184 178 159 139 127 123 121 121
## [50,] 213 184 178 169 154 133 121 121 122 121
## [51,] 215 182 175 168 151 121 124 121 121 121
## [52,] 224 200 182 186 173 154 134 124 121 121
## [53,] 243 223 223 202 191 182 160 142 121 121
## [54,] 265 241 247 233 213 192 177 166 149 137
## [55,] 304 285 274 259 243 223 210 187 170 157
## [56,] 305 304 304 293 272 252 235 211 188 176
## [57,] 305 304 304 304 304 277 261 234 202 182
## [58,] 306 305 304 304 304 298 290 265 220 193
## [59,] 306 305 304 304 304 304 304 304 243 218
## [60,] 305 304 304 304 304 304 304 304 304 243
## [61,] 305 304 304 304 304 304 304 304 283 277
## [62,] 305 304 304 304 304 304 304 304 292 284
## [63,] 304 304 303 304 304 304 304 304 304 304
## [64,] 304 303 301 301 304 304 304 303 304 304
## [65,] 304 299 295 291 296 304 304 300 300 304
## [66,] 304 289 279 270 278 291 304 282 284 294
## [67,] 283 267 251 246 252 267 266 257 263 275
## [68,] 257 255 243 243 243 243 249 242 243 256
## [69,] 244 247 243 243 234 227 224 212 224 237
## [70,] 238 246 248 243 223 199 182 182 198 215
## [71,] 234 254 265 255 233 199 185 182 182 201
## [72,] 231 273 304 304 258 243 182 182 182 182
## [73,] 237 273 304 304 263 243 182 182 181 181
## [74,] 249 270 293 294 254 238 197 182 180 177
## [75,] 233 257 272 264 266 243 200 182 176 168
## [76,] 215 238 251 252 249 245 221 182 159 135
## [77,] 202 226 243 243 245 245 230 182 153 121
## [78,] 192 211 224 237 243 243 238 182 158 121
## [79,] 173 194 206 219 231 243 243 216 182 150
## [80,] 149 173 188 200 213 222 240 233 196 175
## [81,] 129 144 163 182 194 199 221 243 223 182
## [82,] 121 121 142 166 182 182 207 230 243 202
## [83,] 119 120 121 148 162 174 190 212 195 194
## [,328] [,329] [,330] [,331] [,332] [,333] [,334] [,335] [,336] [,337]
## [1,] 367 379 389 395 395 391 380 371 365 352
## [2,] 367 378 388 393 393 391 382 372 367 353
## [3,] 365 375 386 389 391 389 382 374 369 354
## [4,] 358 366 375 382 385 383 379 373 370 365
## [5,] 338 353 363 373 378 378 375 372 370 368
## [6,] 312 329 347 361 369 372 372 371 370 368
## [7,] 301 317 333 350 360 366 369 369 369 367
## [8,] 300 312 323 335 350 359 364 366 367 366
## [9,] 300 308 317 323 334 349 356 360 364 365
## [10,] 292 300 306 308 315 328 341 350 358 363
## [11,] 279 291 291 289 295 307 321 336 350 359
## [12,] 263 269 271 268 275 288 301 313 337 357
## [13,] 243 243 243 243 257 275 294 304 316 338
## [14,] 242 243 243 243 243 260 286 297 304 327
## [15,] 241 242 243 243 243 253 283 297 304 326
## [16,] 242 243 243 243 243 267 297 303 315 330
## [17,] 242 243 243 243 243 266 288 304 312 334
## [18,] 243 243 243 243 243 259 282 295 304 336
## [19,] 239 240 241 242 243 246 272 290 304 327
## [20,] 226 233 238 241 243 251 266 286 304 319
## [21,] 220 229 238 242 243 250 269 282 298 308
## [22,] 217 228 243 242 243 248 262 274 288 304
## [23,] 206 216 231 243 243 245 249 260 273 285
## [24,] 188 191 191 182 213 224 236 243 255 267
## [25,] 183 183 182 184 183 202 214 229 240 249
## [26,] 182 182 182 182 182 182 195 215 230 239
## [27,] 181 181 181 181 182 182 191 209 229 241
## [28,] 178 180 181 182 182 182 202 220 243 241
## [29,] 177 179 181 182 182 182 200 218 229 243
## [30,] 172 178 182 182 182 182 196 211 222 228
## [31,] 166 174 182 182 182 182 189 203 212 219
## [32,] 157 168 176 181 182 182 185 194 202 209
## [33,] 150 162 174 178 182 182 186 190 192 196
## [34,] 146 159 178 181 182 182 182 183 182 182
## [35,] 142 151 159 171 177 181 182 182 182 182
## [36,] 127 129 141 156 171 180 182 182 182 182
## [37,] 121 121 121 145 169 182 182 182 182 182
## [38,] 121 121 136 147 170 182 182 182 182 182
## [39,] 121 121 136 149 165 175 182 182 182 182
## [40,] 121 123 135 146 161 172 176 180 182 182
## [41,] 121 125 133 142 155 166 172 178 182 182
## [42,] 121 126 133 139 151 162 169 176 182 182
## [43,] 121 128 134 140 150 160 167 174 182 182
## [44,] 121 128 134 140 148 157 164 171 182 182
## [45,] 121 126 132 137 144 152 156 161 167 176
## [46,] 121 124 129 133 137 143 146 149 152 156
## [47,] 121 121 123 125 127 131 133 134 133 131
## [48,] 121 121 121 121 122 123 124 124 121 123
## [49,] 121 121 121 121 121 121 121 122 121 121
## [50,] 121 121 121 121 121 121 121 121 121 121
## [51,] 121 121 121 121 121 121 121 121 121 121
## [52,] 121 121 121 121 120 119 120 121 121 121
## [53,] 121 121 120 119 118 115 112 113 121 121
## [54,] 126 121 119 117 115 109 101 93 88 91
## [55,] 143 131 121 121 121 109 94 79 60 65
## [56,] 158 144 134 124 121 121 104 82 60 60
## [57,] 171 155 141 124 121 121 121 92 78 60
## [58,] 178 162 148 127 121 121 112 104 95 78
## [59,] 182 173 167 158 135 121 121 121 121 101
## [60,] 203 182 191 182 161 147 135 129 124 121
## [61,] 243 243 219 192 183 174 152 140 131 124
## [62,] 269 249 243 200 182 166 164 147 134 125
## [63,] 285 265 243 208 183 173 157 143 126 121
## [64,] 304 286 260 228 193 182 162 145 130 121
## [65,] 304 304 269 231 187 180 169 150 125 122
## [66,] 304 279 268 236 208 182 182 164 145 121
## [67,] 278 267 255 248 234 219 201 187 172 146
## [68,] 262 255 249 246 245 243 224 203 182 163
## [69,] 248 249 247 245 243 243 243 230 182 165
## [70,] 232 243 245 244 243 243 243 208 182 172
## [71,] 222 243 243 243 243 233 217 198 192 182
## [72,] 196 231 243 243 243 223 191 185 184 184
## [73,] 182 203 226 243 243 243 182 182 178 150
## [74,] 180 188 212 239 243 243 233 199 176 147
## [75,] 172 182 194 222 243 243 243 243 214 170
## [76,] 152 167 182 208 236 243 243 243 227 176
## [77,] 121 142 164 192 217 228 243 217 207 178
## [78,] 121 121 135 177 200 207 204 201 193 180
## [79,] 121 121 121 136 182 182 182 182 182 158
## [80,] 150 130 121 121 133 137 145 145 133 132
## [81,] 170 153 138 121 121 121 121 121 124 121
## [82,] 182 167 152 129 121 121 121 121 121 122
## [83,] 189 184 175 152 135 134 131 121 121 121
## [,338] [,339] [,340] [,341] [,342] [,343] [,344] [,345] [,346] [,347]
## [1,] 329 314 300 281 271 259 239 214 188 172
## [2,] 329 314 300 289 277 266 254 221 191 173
## [3,] 337 322 307 295 283 269 256 222 192 174
## [4,] 356 338 321 308 294 277 260 222 193 174
## [5,] 365 351 331 318 305 285 266 227 196 176
## [6,] 366 354 333 318 301 284 264 227 199 182
## [7,] 366 353 329 312 297 277 260 232 208 194
## [8,] 366 355 335 316 298 278 258 243 229 219
## [9,] 366 360 346 332 318 301 286 268 255 244
## [10,] 365 364 357 346 335 322 309 297 280 265
## [11,] 364 365 364 358 351 340 327 314 300 280
## [12,] 365 365 365 365 365 359 345 328 309 293
## [13,] 355 365 365 365 365 365 365 339 312 277
## [14,] 348 365 365 365 365 365 365 346 317 294
## [15,] 345 365 365 365 365 365 365 349 321 304
## [16,] 348 365 365 365 365 365 365 350 316 277
## [17,] 354 365 365 365 365 365 365 365 319 284
## [18,] 365 362 364 364 365 365 365 365 333 304
## [19,] 344 361 364 364 365 365 365 365 349 316
## [20,] 333 351 365 365 365 365 366 366 365 345
## [21,] 321 340 359 365 365 365 366 367 367 368
## [22,] 311 328 345 356 365 365 367 368 369 374
## [23,] 298 314 332 344 356 365 368 370 372 382
## [24,] 280 299 317 331 348 365 369 371 376 387
## [25,] 261 287 303 311 336 348 357 361 367 382
## [26,] 243 280 304 318 326 335 341 347 357 365
## [27,] 251 285 303 313 317 320 327 336 348 361
## [28,] 255 290 304 304 304 304 313 322 336 350
## [29,] 243 271 304 290 292 299 304 319 333 343
## [30,] 235 247 253 266 275 282 291 304 319 329
## [31,] 225 235 243 243 259 265 275 291 304 314
## [32,] 216 230 243 247 247 249 260 279 299 304
## [33,] 201 222 243 243 243 243 243 270 304 304
## [34,] 182 206 235 240 242 243 243 255 269 278
## [35,] 182 204 222 234 242 243 243 245 243 256
## [36,] 182 202 221 240 242 243 243 243 243 243
## [37,] 182 198 212 226 243 243 240 242 243 243
## [38,] 182 188 190 205 220 228 238 241 243 243
## [39,] 182 182 183 182 207 219 230 240 243 243
## [40,] 182 182 182 206 201 214 224 238 243 243
## [41,] 182 182 182 201 208 211 217 227 236 238
## [42,] 182 182 182 196 201 206 209 215 220 221
## [43,] 182 182 182 189 193 196 196 202 206 206
## [44,] 182 182 182 182 184 185 182 188 191 191
## [45,] 182 182 182 182 182 183 182 183 184 185
## [46,] 175 182 182 182 182 177 178 181 182 182
## [47,] 147 157 159 159 158 167 172 179 182 182
## [48,] 121 135 136 136 141 150 158 169 182 182
## [49,] 122 121 121 121 131 140 148 159 165 161
## [50,] 121 121 121 121 121 126 134 142 147 141
## [51,] 121 121 121 120 120 121 121 126 127 121
## [52,] 121 121 119 117 116 119 121 122 118 119
## [53,] 121 121 114 109 106 108 109 108 110 113
## [54,] 121 112 103 98 94 95 94 93 101 106
## [55,] 72 89 86 84 82 81 78 78 90 98
## [56,] 61 66 71 71 70 68 64 64 78 89
## [57,] 60 60 60 62 63 60 62 60 66 77
## [58,] 60 60 60 60 60 60 60 60 60 65
## [59,] 71 60 60 60 60 60 60 60 60 60
## [60,] 89 60 60 60 60 60 60 60 60 60
## [61,] 108 74 60 60 60 60 60 60 60 60
## [62,] 110 80 60 60 60 60 60 60 60 60
## [63,] 103 78 60 60 60 60 60 60 60 60
## [64,] 107 71 60 60 60 60 60 60 60 60
## [65,] 95 60 61 60 60 60 60 60 60 60
## [66,] 99 60 60 60 60 60 60 60 60 60
## [67,] 118 60 60 60 60 60 60 60 60 60
## [68,] 130 60 60 60 60 60 60 60 60 60
## [69,] 133 81 60 60 60 60 60 60 60 60
## [70,] 145 121 60 60 60 60 60 60 60 60
## [71,] 153 121 101 60 60 60 60 60 60 60
## [72,] 157 129 121 60 60 60 60 60 60 60
## [73,] 121 121 94 60 60 60 60 60 60 60
## [74,] 125 115 95 60 60 60 60 60 60 60
## [75,] 142 127 121 60 60 60 60 60 60 61
## [76,] 151 134 121 71 60 61 60 60 62 62
## [77,] 154 137 121 60 68 62 61 60 66 67
## [78,] 154 134 121 60 61 62 61 76 81 83
## [79,] 139 121 60 86 64 61 81 97 103 106
## [80,] 130 121 76 60 65 60 90 121 121 121
## [81,] 121 100 94 81 60 60 88 121 121 121
## [82,] 121 105 97 91 77 60 91 89 108 121
## [83,] 121 117 115 113 98 89 65 60 72 77
## [,348] [,349] [,350] [,351] [,352] [,353] [,354] [,355] [,356] [,357]
## [1,] 158 140 122 112 110 110 115 146 173 180
## [2,] 159 141 131 124 117 113 116 147 173 182
## [3,] 159 141 131 125 119 114 117 147 173 187
## [4,] 157 140 129 124 120 117 118 128 148 165
## [5,] 159 141 133 125 123 121 120 122 134 147
## [6,] 174 163 143 131 131 125 122 122 124 137
## [7,] 192 183 173 157 142 131 125 124 126 142
## [8,] 213 201 188 176 157 139 129 127 134 156
## [9,] 235 216 199 182 162 141 130 126 127 135
## [10,] 251 229 205 184 161 142 130 124 123 124
## [11,] 261 224 202 181 157 139 129 124 122 121
## [12,] 264 243 197 178 161 137 121 121 121 121
## [13,] 243 231 210 182 167 150 136 121 121 121
## [14,] 243 224 206 182 173 165 157 144 132 125
## [15,] 243 227 211 199 182 182 182 167 156 145
## [16,] 243 233 224 216 210 212 200 188 176 164
## [17,] 243 243 240 236 234 243 227 209 195 182
## [18,] 272 243 243 242 242 242 243 221 210 206
## [19,] 297 276 258 258 261 252 243 238 232 234
## [20,] 332 304 288 302 307 273 264 243 243 261
## [21,] 367 350 335 349 350 298 309 306 288 292
## [22,] 376 378 381 385 381 365 365 365 304 309
## [23,] 389 397 405 416 415 412 397 384 372 345
## [24,] 398 410 426 423 426 426 426 410 395 380
## [25,] 396 411 426 426 426 426 426 426 418 403
## [26,] 387 406 426 426 426 426 426 426 426 426
## [27,] 371 391 416 426 426 426 426 426 426 426
## [28,] 358 365 391 413 420 426 426 426 426 426
## [29,] 353 365 377 382 398 416 426 426 426 426
## [30,] 339 348 357 362 378 399 413 426 426 426
## [31,] 324 331 338 347 361 380 398 413 426 426
## [32,] 309 311 322 333 349 365 381 396 410 422
## [33,] 304 301 304 316 336 355 365 381 396 411
## [34,] 281 290 297 303 318 344 359 369 381 396
## [35,] 265 278 289 299 304 328 344 356 365 382
## [36,] 250 270 286 302 308 320 332 347 360 369
## [37,] 257 264 279 291 304 313 323 335 346 356
## [38,] 255 265 272 283 294 304 314 328 338 347
## [39,] 251 256 259 269 281 295 304 316 325 334
## [40,] 243 243 243 253 267 281 291 304 313 321
## [41,] 236 230 234 240 249 262 268 282 297 309
## [42,] 218 214 220 227 234 243 243 259 277 291
## [43,] 204 198 205 213 218 229 237 243 259 273
## [44,] 189 182 191 200 203 214 226 236 243 256
## [45,] 185 182 182 187 188 199 215 228 239 243
## [46,] 183 182 181 182 182 182 208 226 243 261
## [47,] 182 181 180 181 182 190 205 225 243 262
## [48,] 170 175 176 180 182 197 213 226 243 259
## [49,] 162 167 172 178 182 197 213 228 243 255
## [50,] 148 155 163 174 182 197 212 227 243 246
## [51,] 133 143 153 169 182 196 211 226 243 243
## [52,] 121 127 140 162 182 192 206 220 235 243
## [53,] 116 120 121 152 173 182 197 206 214 218
## [54,] 112 117 121 143 167 182 186 189 191 192
## [55,] 106 114 121 139 160 171 182 179 181 182
## [56,] 98 108 118 132 152 162 168 174 179 182
## [57,] 88 100 111 127 143 153 162 170 179 182
## [58,] 76 90 103 120 133 143 154 165 177 182
## [59,] 60 78 92 108 121 131 141 153 163 167
## [60,] 60 70 84 102 121 121 131 145 153 157
## [61,] 60 63 75 90 105 114 121 133 139 143
## [62,] 60 60 66 76 93 104 114 121 124 124
## [63,] 60 60 60 63 82 94 106 116 121 121
## [64,] 60 60 60 60 72 83 94 103 108 118
## [65,] 60 60 60 60 68 73 82 91 100 111
## [66,] 60 60 60 60 60 60 70 79 89 105
## [67,] 60 60 60 60 60 60 60 65 75 94
## [68,] 60 60 60 60 60 60 60 60 60 82
## [69,] 60 60 60 60 60 60 60 60 66 75
## [70,] 60 60 60 60 60 60 60 60 60 65
## [71,] 60 60 60 60 60 60 60 60 60 60
## [72,] 60 60 60 60 60 60 60 60 60 60
## [73,] 60 60 60 60 60 60 60 60 60 60
## [74,] 60 60 60 60 60 60 60 60 60 60
## [75,] 60 60 60 60 60 60 60 60 60 60
## [76,] 61 60 60 60 60 60 60 60 60 60
## [77,] 60 60 60 60 60 60 60 60 60 60
## [78,] 73 65 62 61 60 60 60 60 60 59
## [79,] 86 74 67 62 61 60 60 60 60 59
## [80,] 96 80 69 63 61 60 60 60 60 58
## [81,] 102 83 66 62 61 60 60 60 60 58
## [82,] 96 79 61 61 60 60 60 60 60 57
## [83,] 80 73 60 61 60 60 60 60 60 56
## [,358] [,359] [,360] [,361] [,362] [,363] [,364] [,365] [,366] [,367]
## [1,] 182 212 243 263 275 282 265 249 218 202
## [2,] 184 214 243 263 275 279 264 249 218 202
## [3,] 191 217 245 264 276 271 257 240 211 196
## [4,] 189 228 257 270 272 258 247 220 205 193
## [5,] 178 234 273 286 283 265 240 213 196 188
## [6,] 173 235 274 291 290 266 240 212 194 182
## [7,] 174 236 275 291 283 262 237 210 190 178
## [8,] 178 209 250 259 255 243 226 205 186 171
## [9,] 158 189 217 225 218 211 197 184 170 158
## [10,] 139 166 179 192 190 181 175 164 154 145
## [11,] 129 143 155 161 159 154 151 145 138 133
## [12,] 121 125 130 131 130 129 128 126 122 123
## [13,] 121 121 121 121 121 121 121 121 121 127
## [14,] 121 121 121 121 121 121 121 121 121 126
## [15,] 133 121 121 121 121 121 121 121 121 121
## [16,] 149 129 121 121 121 121 121 121 121 182
## [17,] 174 161 131 121 121 121 121 121 126 170
## [18,] 203 188 162 137 121 121 121 121 121 147
## [19,] 233 218 182 159 133 121 121 121 121 129
## [20,] 254 245 205 182 163 143 121 121 121 121
## [21,] 274 250 222 207 192 172 152 126 121 121
## [22,] 304 256 233 227 220 199 182 145 121 121
## [23,] 304 278 254 249 245 229 198 164 131 121
## [24,] 365 297 277 267 255 245 243 176 153 138
## [25,] 385 353 297 282 268 251 236 208 175 160
## [26,] 402 378 365 304 289 269 256 233 204 182
## [27,] 412 382 365 335 304 280 266 249 223 201
## [28,] 420 389 360 339 304 293 280 263 243 224
## [29,] 426 416 387 365 337 304 294 281 259 243
## [30,] 426 426 416 396 379 370 335 305 284 267
## [31,] 426 426 426 426 410 392 377 335 310 291
## [32,] 426 426 426 426 426 410 397 377 347 305
## [33,] 426 426 426 426 426 426 414 393 373 365
## [34,] 415 426 426 426 426 426 426 409 382 365
## [35,] 403 426 426 426 426 426 426 421 395 378
## [36,] 388 408 421 426 426 426 426 426 409 388
## [37,] 372 393 405 426 426 426 426 426 426 408
## [38,] 361 380 387 408 426 426 426 426 426 426
## [39,] 348 359 363 379 407 420 426 426 426 426
## [40,] 335 345 353 360 365 386 411 426 426 426
## [41,] 322 335 343 352 360 365 389 418 426 426
## [42,] 309 324 335 346 356 365 382 404 426 426
## [43,] 294 310 326 339 351 365 375 389 405 419
## [44,] 284 304 316 330 341 351 365 371 382 396
## [45,] 281 304 311 319 326 333 335 347 360 373
## [46,] 290 299 303 306 309 311 311 313 336 346
## [47,] 288 304 303 303 305 305 294 301 312 326
## [48,] 276 291 304 304 289 278 275 286 296 304
## [49,] 268 279 283 279 275 261 261 275 286 296
## [50,] 253 259 261 257 249 245 246 260 273 285
## [51,] 244 246 246 243 244 243 243 243 262 275
## [52,] 243 243 241 240 242 243 243 247 256 268
## [53,] 229 232 235 238 240 242 243 251 259 265
## [54,] 208 222 229 235 240 243 243 250 257 263
## [55,] 191 212 223 233 243 243 243 249 254 260
## [56,] 190 202 214 224 237 243 243 247 250 255
## [57,] 189 192 202 208 219 232 243 243 243 249
## [58,] 183 182 187 189 207 222 234 241 243 243
## [59,] 171 177 179 182 188 209 225 239 243 245
## [60,] 163 171 177 182 193 199 220 243 242 246
## [61,] 149 159 171 182 190 199 209 224 233 236
## [62,] 121 138 158 170 182 190 195 207 210 216
## [63,] 121 127 144 154 162 172 178 188 189 199
## [64,] 121 128 133 137 139 148 162 175 182 182
## [65,] 121 121 122 123 122 128 147 166 177 186
## [66,] 121 121 121 121 121 122 131 153 160 170
## [67,] 108 115 118 120 121 121 131 139 142 149
## [68,] 96 104 110 117 121 121 122 125 121 126
## [69,] 88 98 106 114 121 121 121 121 121 121
## [70,] 76 88 99 110 121 121 118 110 113 117
## [71,] 60 77 89 99 108 121 102 101 106 113
## [72,] 60 68 76 83 90 87 82 73 91 103
## [73,] 60 60 63 66 69 71 64 60 69 85
## [74,] 60 60 60 61 62 62 61 60 60 67
## [75,] 60 60 59 59 60 60 59 59 60 60
## [76,] 59 58 57 56 57 55 57 57 59 63
## [77,] 58 57 55 54 53 52 53 52 54 56
## [78,] 57 55 53 51 50 48 48 46 47 49
## [79,] 56 53 51 48 46 43 42 40 40 41
## [80,] 55 52 49 46 44 40 39 36 35 35
## [81,] 53 50 46 43 40 36 33 29 27 26
## [82,] 52 47 44 40 36 31 26 23 19 17
## [83,] 50 45 41 37 32 26 20 16 11 8
## [,368] [,369] [,370] [,371] [,372] [,373] [,374] [,375] [,376] [,377]
## [1,] 198 191 189 194 194 196 193 192 198 216
## [2,] 191 186 186 186 187 190 187 184 195 214
## [3,] 188 184 184 182 182 185 181 178 185 202
## [4,] 185 181 178 175 175 176 170 169 172 182
## [5,] 181 176 172 167 164 163 159 157 161 167
## [6,] 174 168 162 155 151 149 146 145 149 154
## [7,] 167 158 151 144 139 137 135 134 138 142
## [8,] 159 148 140 134 131 129 126 126 128 130
## [9,] 147 139 132 130 131 130 126 124 125 125
## [10,] 137 133 132 132 136 132 129 130 128 127
## [11,] 131 133 136 138 144 134 147 137 132 148
## [12,] 131 136 143 148 152 185 190 193 194 198
## [13,] 138 156 168 182 184 202 212 225 230 243
## [14,] 129 175 184 191 208 223 236 248 256 258
## [15,] 182 173 192 205 225 243 256 270 285 280
## [16,] 170 188 197 213 237 250 268 288 304 304
## [17,] 182 192 204 218 239 256 272 295 302 303
## [18,] 182 189 199 211 227 243 257 276 293 304
## [19,] 148 171 187 198 215 233 243 261 291 304
## [20,] 121 141 163 182 202 223 235 243 304 302
## [21,] 121 121 140 164 190 213 228 243 284 304
## [22,] 121 121 121 151 186 202 216 229 243 263
## [23,] 121 121 121 129 160 188 200 212 224 236
## [24,] 121 121 121 121 131 161 182 194 206 215
## [25,] 144 129 121 121 121 131 152 172 188 191
## [26,] 167 152 137 121 121 121 121 142 155 167
## [27,] 182 167 152 136 121 121 121 121 138 151
## [28,] 207 192 175 157 130 121 121 121 121 131
## [29,] 228 221 202 182 150 121 121 121 121 121
## [30,] 256 248 233 208 169 121 121 121 121 127
## [31,] 286 270 253 243 195 148 121 121 121 121
## [32,] 306 295 271 250 207 165 148 130 121 121
## [33,] 316 304 292 263 213 182 167 153 137 121
## [34,] 342 306 296 270 233 203 190 175 160 155
## [35,] 365 304 288 256 233 227 220 201 182 182
## [36,] 365 325 299 276 256 252 243 222 209 192
## [37,] 388 365 338 297 286 277 258 249 235 220
## [38,] 406 386 365 320 304 291 279 271 259 243
## [39,] 426 416 396 365 331 313 298 296 292 278
## [40,] 426 426 426 396 365 345 351 365 324 304
## [41,] 426 426 426 421 396 383 383 376 369 352
## [42,] 426 426 426 426 426 426 426 404 385 365
## [43,] 426 426 426 426 428 432 434 430 416 395
## [44,] 409 426 426 426 430 439 448 445 436 426
## [45,] 377 397 416 426 434 449 466 465 455 441
## [46,] 358 365 386 417 438 460 487 487 474 456
## [47,] 345 357 365 402 426 458 487 487 487 464
## [48,] 327 342 359 386 426 443 455 471 478 474
## [49,] 304 323 345 376 406 426 438 450 457 466
## [50,] 296 304 328 363 391 406 420 432 442 456
## [51,] 288 296 304 347 375 392 404 415 426 453
## [52,] 279 289 297 318 365 378 390 402 413 431
## [53,] 274 282 291 301 331 365 376 389 401 420
## [54,] 270 277 285 295 304 332 365 376 388 405
## [55,] 266 273 279 290 299 304 331 365 374 390
## [56,] 261 268 274 284 293 299 304 329 355 376
## [57,] 256 263 269 278 287 294 300 304 332 358
## [58,] 252 259 265 274 283 290 298 304 321 348
## [59,] 249 254 260 267 276 284 293 302 309 339
## [60,] 248 249 252 256 266 277 287 297 304 333
## [61,] 238 239 240 242 250 268 283 297 304 325
## [62,] 222 227 231 238 243 262 281 304 308 314
## [63,] 209 216 227 237 243 258 270 281 293 296
## [64,] 197 206 218 231 243 251 256 260 270 273
## [65,] 190 195 204 215 223 231 235 240 250 251
## [66,] 182 182 188 196 200 201 210 225 233 240
## [67,] 149 151 164 177 181 182 189 211 224 235
## [68,] 121 121 130 161 176 182 194 201 217 235
## [69,] 122 121 121 154 175 182 196 209 219 239
## [70,] 121 121 132 158 182 187 199 212 225 243
## [71,] 121 121 135 158 170 182 199 210 220 236
## [72,] 116 121 135 153 168 182 193 202 210 219
## [73,] 100 112 129 149 164 182 188 192 196 198
## [74,] 86 101 120 137 153 163 175 183 184 172
## [75,] 73 85 105 121 139 147 154 155 152 141
## [76,] 65 67 91 115 126 128 130 128 127 112
## [77,] 60 60 73 99 104 108 107 106 98 85
## [78,] 53 56 67 84 87 89 86 84 72 62
## [79,] 45 48 57 70 69 71 71 67 62 60
## [80,] 38 41 49 60 60 64 64 60 60 61
## [81,] 28 29 35 42 49 54 53 55 57 60
## [82,] 16 17 20 27 32 37 37 44 52 60
## [83,] 4 4 5 13 16 23 25 32 40 50
## [,378] [,379] [,380] [,381] [,382] [,383] [,384] [,385] [,386] [,387]
## [1,] 231 239 242 246 249 262 274 284 294 302
## [2,] 230 233 232 233 237 257 272 281 289 300
## [3,] 215 219 220 215 220 240 251 263 278 291
## [4,] 192 191 195 194 199 210 222 234 249 265
## [5,] 173 178 178 179 183 193 206 218 231 249
## [6,] 158 163 165 169 173 181 192 204 221 235
## [7,] 144 148 153 160 167 174 183 195 211 228
## [8,] 133 135 141 149 158 169 178 190 200 213
## [9,] 125 126 130 137 142 154 168 181 189 199
## [10,] 129 127 124 128 131 137 148 163 175 187
## [11,] 136 133 126 123 123 126 133 151 166 178
## [12,] 192 157 129 121 121 121 121 130 174 180
## [13,] 243 196 155 139 121 121 121 182 182 182
## [14,] 253 209 176 168 175 186 196 217 228 202
## [15,] 268 249 182 182 191 206 220 244 259 255
## [16,] 282 252 182 182 199 212 226 251 274 289
## [17,] 304 268 213 182 203 218 230 257 297 301
## [18,] 304 295 265 243 217 228 235 259 304 306
## [19,] 304 304 294 274 261 259 258 278 304 310
## [20,] 304 304 304 304 304 304 292 299 315 318
## [21,] 304 304 304 304 304 304 304 309 323 330
## [22,] 282 289 304 304 304 304 304 315 330 341
## [23,] 252 268 283 294 300 304 304 317 332 345
## [24,] 225 243 259 269 277 291 304 309 325 338
## [25,] 193 215 235 256 261 275 288 302 317 332
## [26,] 179 182 213 237 243 251 274 297 307 318
## [27,] 176 182 203 226 243 257 265 294 304 306
## [28,] 179 195 206 222 243 252 263 277 292 298
## [29,] 166 189 202 215 227 243 252 259 262 274
## [30,] 147 174 188 200 212 222 236 243 242 252
## [31,] 129 151 166 182 194 199 213 226 237 243
## [32,] 121 129 144 159 170 178 190 206 223 232
## [33,] 121 121 121 136 139 153 169 189 207 215
## [34,] 138 121 121 121 121 129 144 164 188 191
## [35,] 179 182 142 121 121 121 121 132 155 170
## [36,] 188 189 182 148 121 121 121 121 138 145
## [37,] 219 208 196 186 167 133 121 121 121 121
## [38,] 243 228 212 195 182 161 131 121 121 121
## [39,] 267 248 234 208 190 176 158 153 152 152
## [40,] 294 261 243 225 209 197 182 182 182 182
## [41,] 313 281 255 238 226 219 215 216 218 228
## [42,] 342 304 285 265 243 243 243 243 243 245
## [43,] 374 350 319 294 279 272 276 289 292 272
## [44,] 402 381 365 365 304 298 300 314 312 304
## [45,] 425 415 413 391 374 335 329 340 337 323
## [46,] 444 439 434 426 405 384 365 365 365 345
## [47,] 454 452 450 441 426 406 384 367 365 365
## [48,] 469 471 478 475 455 433 405 367 360 331
## [49,] 477 482 487 487 487 449 419 384 365 304
## [50,] 475 484 486 487 469 455 433 393 365 304
## [51,] 487 487 486 487 468 454 433 396 365 304
## [52,] 471 478 478 467 459 450 432 399 365 325
## [53,] 438 451 456 452 448 441 431 411 391 365
## [54,] 421 432 440 438 436 434 431 428 417 397
## [55,] 406 417 426 429 429 430 431 431 430 426
## [56,] 392 405 417 426 426 429 433 436 437 437
## [57,] 377 395 410 422 426 431 436 442 447 452
## [58,] 365 389 406 426 428 433 439 447 455 464
## [59,] 365 380 393 403 417 429 431 443 455 470
## [60,] 365 373 377 382 388 391 405 426 444 464
## [61,] 342 354 357 357 357 359 369 397 418 439
## [62,] 321 331 333 334 334 338 353 365 398 426
## [63,] 300 311 311 312 312 315 338 359 373 393
## [64,] 279 285 292 298 302 304 318 342 352 365
## [65,] 252 263 276 290 301 309 320 326 333 336
## [66,] 243 243 261 285 304 304 307 309 311 311
## [67,] 242 243 253 277 304 304 304 304 304 304
## [68,] 243 243 260 275 285 296 274 274 259 253
## [69,] 242 243 256 267 277 272 258 243 248 244
## [70,] 243 243 247 252 256 251 242 241 242 243
## [71,] 243 243 243 243 243 239 234 237 238 240
## [72,] 231 235 236 235 230 224 227 231 234 238
## [73,] 201 210 216 214 213 212 219 225 229 234
## [74,] 172 189 198 198 198 200 211 217 223 230
## [75,] 121 121 182 182 182 187 201 208 215 223
## [76,] 110 129 123 121 137 175 187 190 192 194
## [77,] 91 103 117 121 136 154 182 164 166 169
## [78,] 69 91 110 121 130 142 146 145 150 156
## [79,] 60 78 102 121 121 124 125 120 128 138
## [80,] 60 75 89 101 121 96 94 105 114 121
## [81,] 60 64 70 72 69 67 68 83 96 109
## [82,] 60 60 60 58 59 60 60 67 81 97
## [83,] 55 55 52 53 55 58 60 60 66 89
## [,388] [,389] [,390] [,391] [,392] [,393] [,394] [,395] [,396] [,397]
## [1,] 306 322 342 357 368 374 371 362 357 357
## [2,] 303 320 341 356 369 377 376 370 367 365
## [3,] 295 311 332 351 368 379 385 380 373 368
## [4,] 281 296 315 343 371 387 399 395 381 370
## [5,] 267 286 305 338 375 402 416 411 390 370
## [6,] 252 269 286 323 363 393 411 398 385 363
## [7,] 241 255 271 294 329 357 370 364 350 337
## [8,] 225 237 251 268 293 315 325 314 306 296
## [9,] 209 216 229 241 256 269 274 273 267 256
## [10,] 194 199 206 216 227 239 239 232 228 225
## [11,] 183 186 190 196 202 203 194 200 197 199
## [12,] 181 182 182 182 182 182 182 184 183 182
## [13,] 182 182 182 182 182 182 182 182 182 187
## [14,] 182 182 182 182 182 182 182 182 182 189
## [15,] 259 250 213 192 182 182 182 182 182 192
## [16,] 304 281 258 243 223 182 182 182 182 182
## [17,] 302 304 280 268 255 247 213 182 182 182
## [18,] 305 304 294 284 276 269 256 243 182 182
## [19,] 315 313 308 299 295 295 280 265 252 213
## [20,] 326 328 324 322 309 310 304 289 281 262
## [21,] 340 346 344 343 340 336 324 314 308 294
## [22,] 355 365 365 365 365 365 349 339 327 315
## [23,] 360 364 365 369 375 377 372 359 347 334
## [24,] 352 365 365 373 386 398 400 390 365 353
## [25,] 347 365 365 377 394 414 426 426 394 365
## [26,] 330 347 365 383 406 426 425 426 427 411
## [27,] 304 324 348 374 398 411 426 426 430 434
## [28,] 300 304 328 362 383 397 411 426 436 459
## [29,] 287 298 304 338 365 379 396 412 426 487
## [30,] 269 285 298 318 341 357 374 393 415 436
## [31,] 252 270 282 298 319 334 350 365 385 405
## [32,] 243 256 268 280 296 312 327 339 352 375
## [33,] 228 243 253 259 267 278 304 309 304 304
## [34,] 206 215 226 230 233 235 240 274 259 279
## [35,] 182 182 182 191 202 211 223 231 240 243
## [36,] 149 160 162 178 182 196 210 222 233 243
## [37,] 121 130 131 150 169 182 194 207 220 232
## [38,] 121 121 121 121 143 162 182 192 205 218
## [39,] 145 130 121 121 121 132 152 172 188 200
## [40,] 182 161 140 121 121 121 121 142 164 182
## [41,] 208 191 172 142 121 121 121 121 140 160
## [42,] 243 222 199 172 142 121 121 121 121 141
## [43,] 257 243 224 198 172 152 130 121 121 126
## [44,] 283 263 243 219 195 182 155 121 121 121
## [45,] 309 294 263 236 209 192 182 151 130 121
## [46,] 320 304 278 250 219 192 182 163 153 126
## [47,] 324 304 282 252 223 182 175 170 166 150
## [48,] 314 299 277 252 231 186 182 181 189 179
## [49,] 296 278 260 245 222 212 203 209 209 201
## [50,] 285 268 243 244 238 232 234 235 235 222
## [51,] 290 276 263 243 243 243 260 263 252 243
## [52,] 300 294 294 286 335 292 292 294 279 262
## [53,] 304 304 335 365 355 365 335 324 304 279
## [54,] 376 335 375 397 411 389 371 365 330 290
## [55,] 406 406 405 426 426 426 393 365 345 293
## [56,] 435 437 441 435 446 426 411 384 365 298
## [57,] 459 470 480 477 487 470 426 400 365 331
## [58,] 475 487 484 487 487 463 454 426 392 356
## [59,] 487 485 486 487 487 472 451 426 409 390
## [60,] 487 487 486 487 487 487 469 447 426 426
## [61,] 487 469 468 481 487 487 480 465 458 455
## [62,] 426 426 435 458 467 474 481 480 480 484
## [63,] 405 398 408 434 448 460 472 486 487 486
## [64,] 365 365 365 398 426 441 456 473 487 487
## [65,] 334 341 349 362 381 416 434 456 470 483
## [66,] 304 318 331 352 365 392 426 442 457 476
## [67,] 286 304 315 345 365 385 426 435 457 487
## [68,] 243 265 297 323 348 365 396 426 435 438
## [69,] 243 243 281 304 337 365 381 390 398 405
## [70,] 243 243 274 304 325 342 357 368 366 374
## [71,] 242 243 272 304 314 327 337 342 343 349
## [72,] 241 243 267 289 304 310 316 319 318 326
## [73,] 239 243 261 278 289 304 304 304 304 304
## [74,] 239 243 254 262 268 271 273 282 294 304
## [75,] 243 243 243 243 243 243 243 260 282 304
## [76,] 195 192 184 198 219 231 243 243 256 279
## [77,] 174 178 182 192 192 212 225 235 241 243
## [78,] 165 173 182 182 182 196 216 226 238 243
## [79,] 148 160 173 180 182 189 205 220 237 247
## [80,] 131 150 169 179 182 196 209 220 239 257
## [81,] 118 139 168 182 191 200 211 224 243 254
## [82,] 111 132 166 182 191 199 207 216 235 249
## [83,] 108 134 176 181 185 189 193 197 203 213
## [,398] [,399] [,400] [,401] [,402] [,403] [,404] [,405] [,406] [,407]
## [1,] 355 356 360 368 376 379 387 397 406 418
## [2,] 362 362 366 372 378 385 392 400 409 419
## [3,] 362 360 364 369 377 383 392 402 412 421
## [4,] 358 348 349 360 369 373 387 405 415 421
## [5,] 352 335 321 339 354 355 373 392 408 413
## [6,] 340 319 306 304 310 323 350 370 380 389
## [7,] 316 297 288 282 290 299 317 341 353 358
## [8,] 283 272 268 266 269 275 286 304 315 326
## [9,] 256 251 252 252 254 256 268 279 288 297
## [10,] 231 236 241 243 244 245 254 259 264 273
## [11,] 211 225 236 240 242 242 245 248 250 255
## [12,] 194 223 235 239 241 242 243 243 243 243
## [13,] 203 223 235 239 242 242 243 243 243 243
## [14,] 200 222 238 243 243 243 243 248 243 243
## [15,] 212 239 242 261 274 279 289 291 270 253
## [16,] 209 231 243 283 304 304 308 313 304 283
## [17,] 199 228 243 304 301 313 324 334 324 311
## [18,] 205 225 235 243 304 321 339 359 349 334
## [19,] 216 227 234 241 274 324 358 363 364 357
## [20,] 238 233 235 239 243 304 365 365 365 365
## [21,] 263 241 240 241 243 273 297 350 365 365
## [22,] 294 270 243 243 264 272 290 314 365 365
## [23,] 317 308 292 281 282 288 294 302 351 365
## [24,] 337 326 316 304 304 304 304 316 339 365
## [25,] 348 338 331 328 325 324 324 333 349 365
## [26,] 370 358 356 356 355 355 355 357 360 377
## [27,] 415 396 396 396 396 396 396 396 402 402
## [28,] 462 457 441 438 438 441 441 441 441 441
## [29,] 485 487 487 472 474 487 487 487 487 487
## [30,] 469 473 474 475 483 486 486 487 480 477
## [31,] 426 441 449 455 471 487 487 471 459 448
## [32,] 382 408 416 423 441 474 481 456 434 424
## [33,] 344 365 388 406 426 441 452 441 426 409
## [34,] 307 340 357 376 396 426 434 437 426 398
## [35,] 290 316 334 353 365 405 427 428 410 375
## [36,] 271 304 321 343 365 386 415 398 385 365
## [37,] 253 279 295 317 349 371 374 375 348 318
## [38,] 236 258 266 284 304 304 304 304 304 291
## [39,] 214 231 238 254 268 273 278 278 269 265
## [40,] 190 201 214 232 243 243 252 252 243 243
## [41,] 177 182 190 213 220 228 233 228 214 198
## [42,] 165 179 182 200 203 207 206 196 182 187
## [43,] 157 182 186 189 190 189 188 183 183 182
## [44,] 137 158 182 182 182 182 181 180 181 181
## [45,] 121 140 154 165 172 175 177 179 181 181
## [46,] 121 121 129 141 157 166 173 179 181 182
## [47,] 121 121 121 121 148 159 170 180 182 191
## [48,] 170 148 137 145 150 159 171 180 182 196
## [49,] 189 182 168 168 165 167 171 178 182 194
## [50,] 210 197 187 182 179 176 176 179 182 190
## [51,] 228 213 196 182 182 182 181 181 181 182
## [52,] 246 234 207 190 182 182 182 182 182 182
## [53,] 252 243 221 207 202 191 182 182 182 182
## [54,] 247 241 230 222 222 218 196 189 184 182
## [55,] 265 243 241 240 243 243 226 209 193 182
## [56,] 276 261 243 243 261 259 243 224 203 182
## [57,] 297 282 282 283 292 293 260 243 224 207
## [58,] 333 304 304 304 302 296 275 259 243 228
## [59,] 381 372 350 330 316 299 281 273 264 252
## [60,] 426 403 383 365 344 314 294 289 287 281
## [61,] 444 432 416 395 374 345 318 303 319 311
## [62,] 471 450 435 426 400 373 365 365 365 342
## [63,] 487 465 447 432 420 402 390 385 377 370
## [64,] 487 471 459 448 437 426 413 404 395 385
## [65,] 480 476 472 462 453 446 432 421 411 401
## [66,] 487 487 487 477 470 468 455 443 426 416
## [67,] 487 487 487 487 481 484 471 464 445 426
## [68,] 441 462 468 476 480 487 487 487 477 442
## [69,] 414 426 426 447 461 487 487 487 449 444
## [70,] 378 379 400 413 420 449 472 465 443 435
## [71,] 352 359 365 382 389 418 440 446 438 434
## [72,] 333 341 350 357 361 386 416 431 434 433
## [73,] 315 325 332 336 341 358 385 411 426 428
## [74,] 304 309 315 317 318 332 365 399 426 426
## [75,] 304 304 304 304 304 321 365 395 426 426
## [76,] 259 272 291 302 304 340 369 390 414 426
## [77,] 247 243 283 304 332 363 374 379 386 404
## [78,] 243 270 284 304 330 355 365 365 365 386
## [79,] 264 280 304 302 323 335 344 348 355 361
## [80,] 267 282 304 304 313 318 326 332 340 347
## [81,] 259 271 283 294 294 301 310 318 326 331
## [82,] 242 255 267 271 273 279 289 304 313 315
## [83,] 204 230 249 250 251 252 255 261 286 298
## [,408] [,409] [,410] [,411] [,412] [,413] [,414] [,415] [,416] [,417]
## [1,] 419 431 434 432 426 420 414 407 403 397
## [2,] 425 433 439 437 432 428 422 416 410 404
## [3,] 426 433 436 434 431 427 422 417 412 406
## [4,] 424 425 426 426 423 420 417 414 411 405
## [5,] 413 413 416 415 410 410 411 411 410 407
## [6,] 391 393 393 396 396 401 404 408 412 415
## [7,] 362 367 369 374 379 388 392 398 412 414
## [8,] 332 338 341 353 361 371 375 382 393 405
## [9,] 303 307 312 323 338 351 354 363 375 385
## [10,] 277 279 282 293 306 319 331 344 357 368
## [11,] 257 257 258 264 282 294 308 326 341 353
## [12,] 243 243 243 243 265 296 304 304 338 351
## [13,] 243 243 243 258 282 304 311 323 336 348
## [14,] 243 243 250 269 297 307 319 331 341 354
## [15,] 243 243 249 276 300 316 331 347 359 367
## [16,] 263 243 264 271 297 320 339 365 363 379
## [17,] 294 283 281 289 297 309 331 349 365 392
## [18,] 319 304 298 297 300 304 321 344 365 395
## [19,] 342 327 312 303 302 304 310 338 365 389
## [20,] 365 350 334 313 304 304 304 324 365 377
## [21,] 367 367 357 344 318 309 304 316 341 365
## [22,] 372 377 381 369 349 334 333 334 349 365
## [23,] 380 386 394 381 365 350 349 350 353 365
## [24,] 390 405 418 401 383 372 362 363 362 362
## [25,] 396 426 425 420 402 393 386 374 365 364
## [26,] 400 426 444 438 420 418 406 400 391 385
## [27,] 413 426 467 465 460 446 426 426 426 426
## [28,] 446 475 484 487 487 487 487 472 458 453
## [29,] 487 487 487 487 487 487 487 487 487 480
## [30,] 474 467 465 467 480 487 487 487 487 487
## [31,] 443 442 442 443 450 462 487 487 487 487
## [32,] 418 415 411 413 416 421 442 468 472 484
## [33,] 393 380 365 374 385 398 411 426 426 451
## [34,] 380 365 338 355 365 381 389 392 413 426
## [35,] 348 317 300 291 298 335 335 335 376 382
## [36,] 304 295 275 252 266 270 274 291 304 325
## [37,] 299 276 258 224 226 232 239 255 257 287
## [38,] 271 257 235 192 182 200 215 224 235 254
## [39,] 261 255 248 198 186 183 190 202 214 232
## [40,] 243 243 243 227 182 182 183 182 195 213
## [41,] 198 198 198 201 187 183 182 182 182 195
## [42,] 183 182 182 182 184 183 182 182 182 182
## [43,] 182 182 182 182 182 183 182 182 190 196
## [44,] 182 182 182 182 182 182 200 208 214 236
## [45,] 182 182 182 182 213 219 219 226 231 248
## [46,] 186 191 211 233 242 246 248 252 257 277
## [47,] 198 213 236 242 247 252 261 278 290 304
## [48,] 209 221 239 248 252 259 274 297 303 315
## [49,] 206 216 229 243 243 243 262 274 304 331
## [50,] 199 206 219 230 236 242 243 243 258 313
## [51,] 189 194 207 222 232 243 243 243 270 287
## [52,] 182 182 193 210 223 234 243 243 267 283
## [53,] 182 182 182 196 213 229 243 243 262 275
## [54,] 182 182 182 182 199 221 243 243 256 267
## [55,] 182 182 182 182 182 206 224 243 249 258
## [56,] 182 182 182 182 182 194 211 227 243 252
## [57,] 193 186 182 182 182 182 190 205 223 245
## [58,] 218 206 188 182 182 182 182 182 205 228
## [59,] 237 225 206 189 182 182 182 182 186 205
## [60,] 262 243 225 210 203 190 182 182 182 182
## [61,] 294 273 245 235 223 212 202 189 182 182
## [62,] 322 304 277 253 243 231 226 212 191 182
## [63,] 355 334 305 281 270 261 253 235 222 196
## [64,] 375 365 335 304 304 304 304 279 250 243
## [65,] 390 380 363 340 336 324 316 304 280 263
## [66,] 406 395 381 365 365 355 352 347 321 311
## [67,] 416 406 391 384 381 381 377 369 365 342
## [68,] 430 421 407 404 404 403 393 380 368 355
## [69,] 434 428 423 426 426 426 411 388 368 339
## [70,] 432 429 427 426 426 426 414 389 355 326
## [71,] 431 429 427 427 426 414 398 378 352 317
## [72,] 432 429 427 427 426 406 387 365 338 304
## [73,] 429 429 427 427 426 407 386 365 336 304
## [74,] 426 427 427 427 426 411 390 365 340 304
## [75,] 426 426 426 426 426 426 402 385 353 304
## [76,] 426 426 426 426 426 426 414 397 374 337
## [77,] 426 426 426 426 426 426 426 419 396 378
## [78,] 398 421 426 426 426 426 426 426 419 408
## [79,] 373 396 419 426 426 426 426 426 426 426
## [80,] 356 373 396 411 426 426 426 426 426 426
## [81,] 341 356 373 388 406 418 423 426 426 426
## [82,] 326 343 359 365 390 400 408 412 423 426
## [83,] 310 331 352 365 377 386 393 398 402 409
## [,418] [,419] [,420] [,421] [,422] [,423] [,424] [,425] [,426] [,427]
## [1,] 388 378 368 355 345 333 325 313 302 295
## [2,] 392 380 371 362 352 342 330 317 304 298
## [3,] 392 380 371 362 354 344 331 317 304 299
## [4,] 390 377 369 362 355 342 326 314 309 305
## [5,] 393 378 371 365 358 347 334 323 317 316
## [6,] 410 396 380 372 364 354 343 334 329 327
## [7,] 418 416 398 382 371 362 352 345 342 340
## [8,] 410 401 390 380 373 368 361 356 353 351
## [9,] 396 392 382 377 374 371 367 364 362 360
## [10,] 380 380 376 376 376 373 370 367 365 365
## [11,] 367 371 372 376 380 377 378 369 366 365
## [12,] 360 365 367 381 391 399 391 370 365 365
## [13,] 359 365 377 397 419 424 417 395 372 365
## [14,] 362 383 396 414 426 426 424 418 389 375
## [15,] 382 404 419 424 424 425 426 423 402 386
## [16,] 405 426 423 425 424 425 426 420 400 390
## [17,] 421 424 425 425 425 425 426 415 398 385
## [18,] 426 426 426 425 426 426 426 419 399 385
## [19,] 421 426 426 426 426 426 427 424 410 397
## [20,] 415 426 426 426 427 427 428 427 426 414
## [21,] 411 426 426 426 427 428 429 429 427 426
## [22,] 409 426 426 427 428 430 432 431 429 427
## [23,] 406 426 426 428 430 433 435 434 429 426
## [24,] 382 426 426 432 439 445 450 446 427 418
## [25,] 380 411 426 445 461 473 487 487 426 408
## [26,] 397 412 426 454 480 485 479 453 426 414
## [27,] 421 420 426 458 469 487 458 440 436 426
## [28,] 445 444 451 461 457 446 435 432 430 427
## [29,] 483 487 487 487 458 426 427 423 426 426
## [30,] 496 517 499 487 481 451 424 413 403 403
## [31,] 492 494 491 493 487 452 422 398 380 365
## [32,] 487 489 488 480 466 453 433 395 365 368
## [33,] 465 466 465 462 455 448 432 400 382 365
## [34,] 444 446 451 449 447 441 430 405 383 365
## [35,] 408 420 432 435 435 433 423 401 383 365
## [36,] 365 387 408 426 428 426 405 390 379 365
## [37,] 321 350 375 382 405 394 386 378 369 363
## [38,] 285 304 327 352 365 365 365 365 342 349
## [39,] 254 274 294 315 330 334 330 316 314 317
## [40,] 231 243 263 284 304 304 304 300 301 303
## [41,] 213 229 240 253 256 271 271 284 295 301
## [42,] 194 218 231 238 242 243 243 273 290 300
## [43,] 199 212 227 237 241 243 254 274 294 304
## [44,] 243 232 232 243 243 265 275 298 312 327
## [45,] 252 243 243 260 280 280 298 318 334 350
## [46,] 280 281 292 290 300 304 322 338 357 366
## [47,] 304 304 309 304 304 317 334 349 365 374
## [48,] 334 340 341 350 350 353 352 355 359 365
## [49,] 365 365 365 362 365 366 365 361 362 365
## [50,] 355 365 365 365 365 368 370 368 365 399
## [51,] 304 304 345 365 365 371 378 381 401 426
## [52,] 291 297 302 321 350 372 385 394 406 426
## [53,] 283 288 293 299 304 350 376 388 400 410
## [54,] 277 282 288 293 298 320 365 377 389 398
## [55,] 269 274 279 284 289 298 320 350 371 374
## [56,] 260 265 271 275 279 287 297 304 327 352
## [57,] 252 257 263 266 268 275 286 293 301 315
## [58,] 243 249 254 256 258 263 275 282 290 298
## [59,] 220 234 246 247 247 251 264 272 280 288
## [60,] 197 205 217 222 223 237 252 260 269 278
## [61,] 182 182 191 192 192 198 229 248 257 267
## [62,] 182 182 182 182 182 182 182 218 243 254
## [63,] 182 182 182 182 182 182 182 190 217 236
## [64,] 219 213 195 182 182 182 182 182 199 219
## [65,] 243 243 220 200 182 182 182 182 191 211
## [66,] 291 284 257 233 208 182 182 182 182 205
## [67,] 320 307 304 273 243 188 182 182 182 205
## [68,] 332 312 305 274 231 183 183 182 198 212
## [69,] 318 304 275 243 211 182 182 182 201 220
## [70,] 304 285 267 243 198 182 182 182 195 213
## [71,] 304 280 260 243 186 183 183 182 182 196
## [72,] 285 266 249 233 190 183 183 182 182 182
## [73,] 274 243 246 225 207 182 182 182 182 182
## [74,] 280 254 243 238 223 211 198 192 186 182
## [75,] 292 276 279 260 243 230 218 215 205 200
## [76,] 304 289 303 295 275 243 231 229 218 215
## [77,] 371 335 349 347 331 296 278 264 237 236
## [78,] 402 399 396 386 371 365 365 365 304 304
## [79,] 427 427 427 417 413 411 411 406 383 372
## [80,] 428 430 431 434 439 446 446 435 426 405
## [81,] 429 434 437 446 460 477 477 462 447 433
## [82,] 432 439 445 454 477 484 487 487 472 456
## [83,] 420 431 433 446 470 487 487 487 487 479
## [,428] [,429] [,430] [,431] [,432] [,433] [,434] [,435] [,436] [,437]
## [1,] 288 281 273 259 249 237 224 215 211 216
## [2,] 295 290 279 266 253 242 234 227 222 223
## [3,] 298 295 281 266 253 244 237 230 227 227
## [4,] 306 304 296 279 260 251 243 239 236 236
## [5,] 316 313 308 297 280 262 254 253 250 250
## [6,] 327 323 316 308 298 285 273 270 270 271
## [7,] 338 332 323 314 306 299 291 292 289 291
## [8,] 348 339 328 317 309 305 302 302 302 303
## [9,] 357 346 332 319 310 306 304 304 304 305
## [10,] 362 349 331 318 310 306 304 303 302 304
## [11,] 360 348 331 317 308 304 302 299 295 296
## [12,] 365 346 327 306 304 299 294 289 284 284
## [13,] 365 350 330 311 304 290 279 265 254 253
## [14,] 365 356 336 311 292 283 267 243 247 244
## [15,] 373 365 337 307 295 284 275 264 251 244
## [16,] 376 365 338 314 304 295 291 280 271 268
## [17,] 369 360 345 334 322 314 309 298 296 295
## [18,] 365 358 353 351 347 338 331 324 320 314
## [19,] 388 373 364 367 365 359 356 345 343 327
## [20,] 409 395 384 371 367 365 365 365 365 337
## [21,] 426 418 395 376 367 365 351 345 332 331
## [22,] 426 405 395 371 365 337 324 314 300 295
## [23,] 412 397 378 361 338 324 304 293 277 266
## [24,] 401 381 365 348 326 304 293 276 252 244
## [25,] 390 365 367 347 325 304 294 278 263 244
## [26,] 398 385 371 356 334 321 309 297 276 255
## [27,] 410 397 384 369 348 332 317 304 292 267
## [28,] 423 411 397 376 361 343 327 311 300 279
## [29,] 427 426 410 388 365 356 341 324 304 291
## [30,] 418 426 422 400 379 369 359 343 326 305
## [31,] 387 409 426 413 388 379 372 365 344 323
## [32,] 366 379 426 406 393 384 377 365 355 335
## [33,] 365 365 382 390 394 395 395 391 374 352
## [34,] 365 365 365 382 400 408 417 426 405 375
## [35,] 365 364 365 386 403 414 426 425 426 406
## [36,] 364 364 365 391 409 417 426 426 426 426
## [37,] 362 363 365 416 426 424 416 419 426 426
## [38,] 354 359 365 426 426 426 402 392 401 426
## [39,] 335 351 375 410 411 394 375 366 363 379
## [40,] 304 331 359 381 380 377 365 358 351 314
## [41,] 304 310 354 366 370 370 366 359 341 312
## [42,] 304 327 352 367 369 368 367 366 365 339
## [43,] 319 331 356 370 370 369 367 366 366 357
## [44,] 338 346 360 374 374 371 367 365 365 358
## [45,] 365 365 377 391 382 373 365 366 361 342
## [46,] 380 394 421 426 406 386 372 365 355 325
## [47,] 391 413 426 426 426 406 388 375 365 336
## [48,] 398 426 425 426 426 421 401 385 369 341
## [49,] 399 426 426 426 426 426 407 390 371 355
## [50,] 416 422 425 426 426 414 399 386 373 366
## [51,] 422 425 425 405 389 393 382 378 373 368
## [52,] 426 425 402 375 357 350 354 361 368 367
## [53,] 426 426 380 345 324 304 322 337 358 365
## [54,] 411 426 379 324 304 311 304 320 333 324
## [55,] 389 385 374 304 306 305 305 304 308 300
## [56,] 365 371 368 336 304 304 304 303 298 288
## [57,] 336 357 366 345 315 304 304 302 291 277
## [58,] 304 331 365 365 334 304 304 299 284 267
## [59,] 296 311 357 365 358 333 313 301 284 263
## [60,] 288 300 331 365 365 353 335 317 294 270
## [61,] 277 292 304 333 357 365 357 332 298 278
## [62,] 265 284 304 316 341 356 365 365 301 286
## [63,] 249 272 298 304 334 353 361 356 318 294
## [64,] 234 261 304 319 332 354 365 352 315 296
## [65,] 229 258 304 325 343 365 361 365 317 296
## [66,] 225 259 304 327 348 365 365 365 319 295
## [67,] 224 259 304 334 356 359 365 337 316 297
## [68,] 229 262 304 355 365 364 331 314 311 306
## [69,] 243 284 318 365 365 331 304 306 305 305
## [70,] 234 260 290 298 316 314 291 284 292 299
## [71,] 212 234 259 266 270 267 261 259 267 273
## [72,] 190 197 213 228 228 233 239 243 249 247
## [73,] 182 182 182 182 182 200 227 239 242 242
## [74,] 182 182 182 182 182 182 223 237 241 242
## [75,] 198 197 192 182 182 224 226 237 240 242
## [76,] 213 212 210 210 219 227 234 237 240 242
## [77,] 236 234 237 238 243 238 236 238 240 242
## [78,] 263 258 274 267 256 247 243 241 241 242
## [79,] 335 335 314 293 276 257 243 243 242 242
## [80,] 391 376 365 331 304 272 243 243 243 243
## [81,] 418 397 376 365 322 297 276 249 243 243
## [82,] 441 417 389 365 350 330 304 274 243 243
## [83,] 464 441 416 396 375 356 336 304 274 253
## [,438] [,439] [,440] [,441] [,442] [,443] [,444] [,445] [,446] [,447]
## [1,] 218 230 235 250 249 267 285 295 311 324
## [2,] 227 234 239 252 251 268 285 297 314 326
## [3,] 231 236 241 253 253 272 287 305 318 326
## [4,] 238 240 243 247 260 274 292 305 317 319
## [5,] 252 253 254 258 271 287 305 319 331 327
## [6,] 269 272 271 275 289 301 319 337 345 343
## [7,] 292 292 295 297 309 322 340 350 357 355
## [8,] 305 307 309 319 331 344 352 359 362 362
## [9,] 310 316 323 338 351 354 359 361 362 363
## [10,] 309 317 331 348 352 356 358 352 356 360
## [11,] 297 306 319 336 349 345 346 335 338 351
## [12,] 284 293 304 304 325 330 333 313 304 324
## [13,] 253 261 257 278 295 309 308 307 302 304
## [14,] 243 243 245 243 264 277 285 292 296 304
## [15,] 243 243 243 243 243 251 263 267 271 278
## [16,] 258 243 243 243 243 243 243 243 243 243
## [17,] 287 265 251 243 243 243 240 229 217 208
## [18,] 306 289 274 259 246 243 236 214 196 182
## [19,] 313 305 297 269 254 246 240 214 182 184
## [20,] 317 307 304 275 255 245 244 243 182 182
## [21,] 315 307 304 276 254 243 243 213 207 182
## [22,] 294 289 272 253 243 245 243 213 196 190
## [23,] 264 259 252 250 245 243 243 214 194 185
## [24,] 242 246 245 244 245 243 229 209 188 180
## [25,] 237 227 213 213 213 206 192 182 178 169
## [26,] 237 216 193 182 182 182 183 174 165 156
## [27,] 243 231 215 205 197 190 182 174 169 162
## [28,] 260 249 236 224 219 213 206 199 198 193
## [29,] 274 264 253 243 238 235 234 243 243 225
## [30,] 289 279 268 257 248 244 243 242 243 213
## [31,] 304 294 282 268 257 246 243 216 182 198
## [32,] 316 304 291 275 261 243 243 222 204 182
## [33,] 332 318 304 290 276 267 252 237 222 217
## [34,] 350 335 320 304 292 283 268 253 243 243
## [35,] 375 358 342 327 312 299 284 268 262 256
## [36,] 406 385 365 350 335 320 299 284 275 267
## [37,] 426 416 380 368 358 340 314 299 289 279
## [38,] 426 381 380 371 368 357 334 317 304 293
## [39,] 377 370 369 367 366 366 357 332 318 308
## [40,] 335 345 365 348 353 365 365 341 326 316
## [41,] 304 304 304 316 317 329 346 340 329 319
## [42,] 310 304 304 304 304 304 304 314 319 316
## [43,] 321 309 305 304 304 302 302 304 308 311
## [44,] 322 312 307 305 304 295 294 297 302 305
## [45,] 314 304 304 304 296 282 285 288 293 299
## [46,] 306 306 302 296 287 270 275 277 283 291
## [47,] 304 305 299 290 277 254 257 259 268 277
## [48,] 326 311 300 288 272 247 243 243 250 262
## [49,] 342 328 315 304 287 254 243 243 243 243
## [50,] 359 343 326 313 304 269 243 243 243 243
## [51,] 365 356 335 318 304 275 243 243 243 243
## [52,] 366 353 336 319 304 277 243 243 243 243
## [53,] 329 327 321 315 310 286 243 243 243 243
## [54,] 304 304 314 311 308 287 256 243 243 243
## [55,] 296 295 296 298 296 272 256 250 245 243
## [56,] 281 278 274 278 276 268 256 249 243 244
## [57,] 267 259 251 260 261 258 253 248 243 243
## [58,] 253 243 246 243 248 249 248 246 243 243
## [59,] 249 244 243 244 243 243 243 243 243 243
## [60,] 259 252 243 243 243 243 243 243 243 243
## [61,] 268 259 252 246 243 243 243 243 243 243
## [62,] 276 267 259 252 245 243 243 243 243 243
## [63,] 284 272 263 255 246 243 243 243 243 243
## [64,] 287 277 267 258 248 243 243 243 243 243
## [65,] 287 278 269 259 249 243 243 243 243 243
## [66,] 286 275 265 254 245 244 244 243 243 243
## [67,] 287 273 259 243 244 244 243 244 243 243
## [68,] 298 278 261 247 243 243 243 243 243 243
## [69,] 304 285 267 252 243 243 243 243 243 243
## [70,] 304 274 260 247 243 243 243 243 243 243
## [71,] 260 243 243 245 243 243 243 243 243 243
## [72,] 244 245 243 243 243 243 243 243 243 243
## [73,] 243 243 243 243 243 243 243 243 243 243
## [74,] 242 242 242 243 243 243 243 243 243 243
## [75,] 242 242 242 243 243 243 243 246 243 243
## [76,] 242 242 242 243 243 243 253 258 256 243
## [77,] 243 243 243 243 243 243 264 281 291 291
## [78,] 243 243 243 243 243 243 277 304 308 309
## [79,] 243 243 247 246 243 260 294 310 323 327
## [80,] 243 243 253 259 249 284 304 325 340 349
## [81,] 243 243 265 279 289 311 324 341 359 367
## [82,] 243 243 284 304 311 331 344 365 370 380
## [83,] 243 260 304 320 339 347 353 365 381 396
## [,448] [,449] [,450] [,451] [,452] [,453] [,454] [,455] [,456] [,457]
## [1,] 317 314 305 284 265 253 243 233 222 211
## [2,] 318 315 306 284 265 253 242 234 227 223
## [3,] 316 314 300 273 261 250 242 235 229 226
## [4,] 314 309 297 280 261 250 243 237 232 230
## [5,] 316 312 299 283 264 252 246 241 236 234
## [6,] 334 323 309 295 283 269 255 250 242 239
## [7,] 349 339 325 313 304 295 279 262 250 244
## [8,] 360 353 341 327 313 307 297 283 266 254
## [9,] 364 363 353 336 322 311 300 290 275 259
## [10,] 363 365 357 339 321 312 303 291 277 261
## [11,] 362 365 361 341 325 313 306 298 285 267
## [12,] 365 365 365 351 315 308 306 305 304 289
## [13,] 332 355 365 339 309 306 305 304 304 304
## [14,] 316 331 365 322 304 304 304 304 304 304
## [15,] 287 289 289 279 260 259 259 279 292 299
## [16,] 243 243 243 213 213 225 235 243 260 273
## [17,] 198 198 192 189 182 199 213 224 236 247
## [18,] 186 182 180 181 181 182 194 202 210 232
## [19,] 183 181 178 176 172 178 182 185 187 185
## [20,] 182 178 175 169 154 161 170 182 182 178
## [21,] 182 177 173 162 139 148 155 158 160 170
## [22,] 184 179 177 155 128 128 130 131 139 151
## [23,] 184 183 182 167 135 121 121 121 121 128
## [24,] 176 175 172 153 135 128 123 121 119 119
## [25,] 156 153 148 142 133 127 123 121 117 113
## [26,] 130 129 126 128 124 122 121 117 114 103
## [27,] 151 121 121 121 121 121 121 121 121 103
## [28,] 186 183 167 167 172 180 182 167 137 119
## [29,] 196 185 182 182 182 182 182 161 153 127
## [30,] 189 184 181 176 171 154 148 153 141 127
## [31,] 182 182 178 168 159 121 121 128 127 121
## [32,] 182 182 182 182 182 161 135 121 121 121
## [33,] 214 213 213 213 206 188 172 163 155 162
## [34,] 243 243 243 243 243 205 191 182 182 188
## [35,] 251 247 243 243 218 209 199 194 194 198
## [36,] 258 250 243 243 222 212 205 201 202 206
## [37,] 268 258 245 243 227 219 212 208 210 213
## [38,] 281 270 250 243 234 227 219 216 217 220
## [39,] 298 286 264 248 241 235 226 223 225 227
## [40,] 309 304 277 259 249 243 234 231 231 235
## [41,] 311 304 285 264 253 243 238 236 236 238
## [42,] 311 304 289 272 261 249 243 242 243 241
## [43,] 309 304 294 281 273 266 263 261 252 243
## [44,] 305 305 302 292 288 284 283 278 266 256
## [45,] 304 304 305 304 304 304 304 292 278 264
## [46,] 300 304 305 313 320 325 321 310 294 279
## [47,] 287 297 307 322 337 348 346 333 309 294
## [48,] 274 286 304 332 358 365 365 357 318 306
## [49,] 257 271 295 324 365 365 365 331 319 309
## [50,] 243 258 281 296 318 343 339 329 317 309
## [51,] 243 243 258 274 289 304 315 316 313 307
## [52,] 243 243 243 258 274 289 304 304 304 304
## [53,] 243 243 243 243 251 266 270 269 263 255
## [54,] 243 243 243 243 243 243 243 243 245 243
## [55,] 243 243 243 243 243 243 243 243 243 243
## [56,] 243 243 243 243 243 243 243 243 243 243
## [57,] 243 243 243 243 243 243 243 243 243 243
## [58,] 243 243 243 243 243 243 243 243 243 243
## [59,] 243 243 243 243 243 243 243 243 243 265
## [60,] 243 243 243 243 243 243 247 246 257 284
## [61,] 243 243 243 243 243 243 253 257 279 299
## [62,] 243 243 243 243 243 254 261 269 288 299
## [63,] 243 243 243 243 247 258 268 284 296 301
## [64,] 243 243 243 243 250 264 279 300 304 304
## [65,] 243 243 243 243 243 263 276 296 304 304
## [66,] 243 243 243 243 246 254 261 279 299 304
## [67,] 243 243 243 243 243 243 243 261 288 298
## [68,] 243 243 243 243 243 243 243 246 282 294
## [69,] 243 243 243 243 243 243 243 258 282 293
## [70,] 243 243 243 243 243 250 256 268 285 293
## [71,] 243 243 243 243 256 265 271 281 292 298
## [72,] 243 244 252 260 271 282 288 296 305 309
## [73,] 243 246 262 274 291 304 304 305 312 320
## [74,] 243 252 263 279 304 301 304 307 317 327
## [75,] 243 243 250 264 279 297 304 309 325 335
## [76,] 243 243 243 243 258 281 297 310 328 339
## [77,] 261 243 243 243 243 274 300 311 327 338
## [78,] 294 263 243 243 243 275 304 316 330 341
## [79,] 317 294 274 264 275 284 299 316 338 351
## [80,] 344 323 304 304 295 293 298 316 346 365
## [81,] 370 355 340 324 312 302 302 326 351 365
## [82,] 388 380 365 350 342 339 337 355 365 407
## [83,] 412 414 394 379 374 369 356 369 398 426
## [,458] [,459] [,460] [,461] [,462] [,463] [,464] [,465] [,466] [,467]
## [1,] 216 217 220 216 202 187 180 155 136 126
## [2,] 223 227 229 226 207 193 187 159 141 130
## [3,] 227 231 233 231 225 204 194 183 155 136
## [4,] 232 236 239 240 236 224 206 190 176 161
## [5,] 235 239 241 242 242 237 228 212 198 188
## [6,] 238 240 242 242 243 243 241 230 221 206
## [7,] 242 241 242 242 243 243 243 241 234 217
## [8,] 246 243 242 243 243 243 243 243 239 219
## [9,] 249 245 243 243 243 243 243 243 240 214
## [10,] 251 246 243 243 243 243 243 243 243 233
## [11,] 256 246 243 244 244 244 243 243 243 240
## [12,] 273 243 243 249 246 245 243 243 243 243
## [13,] 299 279 272 260 252 247 243 243 243 242
## [14,] 304 304 290 275 262 252 243 243 243 242
## [15,] 304 304 304 285 270 258 247 243 243 241
## [16,] 284 304 284 281 271 262 248 243 243 239
## [17,] 242 253 263 263 261 259 255 243 243 236
## [18,] 225 234 243 247 250 259 265 253 243 223
## [19,] 194 212 233 243 245 264 278 263 250 243
## [20,] 182 191 216 232 243 281 300 278 256 243
## [21,] 177 182 202 222 243 304 304 304 257 243
## [22,] 165 176 187 204 223 243 294 274 233 195
## [23,] 146 158 166 182 202 221 243 223 182 188
## [24,] 128 140 134 157 171 192 194 176 174 175
## [25,] 113 121 93 134 132 143 153 153 160 160
## [26,] 90 69 63 91 80 101 116 133 136 134
## [27,] 80 60 60 62 60 60 91 121 121 92
## [28,] 90 78 66 60 60 60 60 71 63 61
## [29,] 101 90 81 73 60 60 60 60 60 61
## [30,] 106 99 92 85 84 66 60 60 60 60
## [31,] 116 112 110 107 112 108 93 79 72 65
## [32,] 121 121 121 121 138 137 121 106 103 89
## [33,] 183 187 186 170 170 171 149 135 126 113
## [34,] 195 201 204 208 213 204 182 166 151 145
## [35,] 209 217 226 237 242 238 225 197 175 173
## [36,] 219 227 235 238 243 243 243 243 212 194
## [37,] 226 233 239 241 242 243 243 237 233 228
## [38,] 231 237 241 242 243 243 243 243 243 243
## [39,] 236 240 242 243 243 243 243 243 243 243
## [40,] 239 242 243 243 243 243 243 243 243 243
## [41,] 241 242 243 243 243 243 243 243 243 243
## [42,] 243 243 243 243 243 243 243 243 243 243
## [43,] 244 243 243 243 243 243 243 243 243 243
## [44,] 250 244 243 243 243 243 243 243 243 243
## [45,] 255 243 243 243 243 243 243 243 243 243
## [46,] 268 258 249 244 243 243 243 243 243 243
## [47,] 283 270 259 249 243 243 243 243 243 243
## [48,] 299 283 267 246 245 243 243 243 243 243
## [49,] 306 304 285 259 243 244 243 243 243 243
## [50,] 306 305 293 267 243 243 244 243 243 243
## [51,] 304 288 276 259 243 243 243 243 243 243
## [52,] 284 276 265 254 243 244 243 243 243 243
## [53,] 256 251 249 244 245 244 243 243 243 243
## [54,] 243 243 243 243 244 244 243 243 243 243
## [55,] 243 243 243 243 243 243 243 243 243 243
## [56,] 243 243 243 243 243 243 243 243 243 243
## [57,] 243 243 243 243 243 243 243 243 243 243
## [58,] 243 243 243 274 250 243 243 243 243 243
## [59,] 277 289 294 302 285 268 256 254 253 253
## [60,] 304 300 308 310 306 304 287 285 284 284
## [61,] 302 304 313 320 327 316 304 304 304 304
## [62,] 301 304 320 332 349 352 329 304 304 304
## [63,] 304 316 325 339 360 361 365 335 304 304
## [64,] 304 318 332 346 365 365 364 365 350 323
## [65,] 304 317 328 341 358 365 365 365 365 365
## [66,] 304 312 318 329 344 361 365 365 365 365
## [67,] 304 304 304 314 329 349 359 365 365 365
## [68,] 299 302 303 304 314 342 353 359 364 365
## [69,] 297 300 302 303 304 338 349 356 362 364
## [70,] 298 300 302 304 318 337 347 355 362 365
## [71,] 304 304 304 319 333 341 350 357 365 364
## [72,] 314 314 321 330 344 350 354 359 362 365
## [73,] 327 331 339 348 360 360 361 363 364 364
## [74,] 336 346 356 365 366 365 364 364 365 365
## [75,] 347 360 364 367 373 377 374 375 378 385
## [76,] 350 357 365 371 387 395 398 405 409 410
## [77,] 348 357 362 375 400 418 421 426 427 423
## [78,] 351 359 365 386 407 416 426 431 431 436
## [79,] 361 369 379 394 411 419 426 436 440 445
## [80,] 371 381 392 409 426 426 436 443 449 455
## [81,] 382 393 402 417 425 434 443 451 459 464
## [82,] 394 402 408 417 426 441 452 462 472 473
## [83,] 417 412 413 419 426 447 463 475 487 480
## [,468] [,469] [,470] [,471] [,472] [,473] [,474] [,475] [,476] [,477]
## [1,] 134 130 123 114 103 94 88 76 67 62
## [2,] 134 139 131 120 109 102 95 81 71 64
## [3,] 139 141 132 120 112 109 100 92 77 69
## [4,] 148 142 136 129 135 122 117 104 95 80
## [5,] 178 165 164 163 164 147 135 122 113 99
## [6,] 192 179 174 177 179 172 162 144 128 115
## [7,] 201 190 183 181 180 179 166 152 134 122
## [8,] 200 189 183 177 172 168 153 142 124 112
## [9,] 200 188 177 165 158 147 140 130 102 87
## [10,] 207 188 170 147 137 137 132 117 98 79
## [11,] 216 197 180 166 151 138 133 127 112 94
## [12,] 214 207 195 181 182 161 149 138 129 121
## [13,] 216 204 198 191 188 185 174 162 151 138
## [14,] 218 208 203 201 200 196 190 182 170 154
## [15,] 221 214 211 210 212 210 205 198 188 168
## [16,] 225 220 219 220 224 224 222 218 210 179
## [17,] 221 222 224 234 243 243 243 243 243 212
## [18,] 182 202 212 225 243 243 243 243 243 243
## [19,] 182 182 196 212 229 243 241 243 243 243
## [20,] 182 182 185 191 206 219 232 238 243 233
## [21,] 182 183 182 182 182 208 225 233 243 196
## [22,] 188 183 182 182 197 212 230 225 210 192
## [23,] 181 186 183 197 213 233 243 213 198 186
## [24,] 177 179 189 210 236 241 243 192 182 170
## [25,] 165 170 187 203 215 243 182 185 170 160
## [26,] 135 139 175 184 186 175 172 162 157 149
## [27,] 91 111 131 150 158 155 151 148 144 137
## [28,] 60 76 112 104 136 136 137 135 133 127
## [29,] 60 60 60 60 121 121 125 126 125 123
## [30,] 60 60 60 60 60 60 121 121 121 109
## [31,] 60 60 60 60 60 60 60 76 76 72
## [32,] 84 81 75 60 60 60 60 60 60 60
## [33,] 112 112 104 93 79 72 66 60 60 60
## [34,] 138 137 126 121 105 103 97 94 81 81
## [35,] 162 160 154 145 134 130 128 124 112 111
## [36,] 182 182 182 182 165 155 147 138 130 122
## [37,] 229 228 228 223 196 176 164 153 140 122
## [38,] 242 243 243 243 243 200 182 170 158 147
## [39,] 243 243 243 242 215 208 193 182 174 164
## [40,] 243 243 242 238 218 204 197 190 184 182
## [41,] 243 243 242 235 220 209 200 192 185 182
## [42,] 243 243 239 230 223 213 204 194 183 182
## [43,] 243 243 235 228 221 214 206 196 182 182
## [44,] 243 243 236 230 225 220 216 206 192 182
## [45,] 243 243 239 235 232 232 231 219 203 191
## [46,] 243 243 243 242 242 243 243 231 214 205
## [47,] 243 243 243 243 243 243 243 243 225 220
## [48,] 243 243 243 243 243 243 243 240 237 237
## [49,] 243 243 243 243 243 243 243 243 243 242
## [50,] 243 243 243 243 243 243 243 243 243 243
## [51,] 243 243 243 243 243 243 243 243 243 243
## [52,] 243 243 243 243 243 243 243 243 243 243
## [53,] 243 243 243 243 243 243 243 243 243 243
## [54,] 243 243 243 243 243 243 243 243 243 243
## [55,] 243 243 243 243 243 243 243 243 243 243
## [56,] 243 243 243 243 243 243 243 243 243 243
## [57,] 243 243 243 243 243 243 243 243 243 243
## [58,] 243 243 243 243 243 243 243 243 243 243
## [59,] 249 243 243 243 243 243 243 243 243 243
## [60,] 279 249 243 243 243 243 243 243 243 243
## [61,] 304 254 243 243 243 243 243 243 243 243
## [62,] 288 265 243 243 243 243 243 243 243 243
## [63,] 295 282 260 243 243 243 243 243 243 243
## [64,] 315 303 279 258 243 243 243 243 243 243
## [65,] 340 314 304 271 243 243 243 243 243 243
## [66,] 360 331 304 287 270 257 256 249 243 243
## [67,] 365 365 336 304 289 282 272 258 243 243
## [68,] 365 365 365 340 315 299 288 273 259 249
## [69,] 365 365 366 365 340 322 304 289 276 268
## [70,] 365 365 368 367 359 343 328 306 294 290
## [71,] 365 369 374 374 371 365 350 333 304 304
## [72,] 365 373 379 381 378 373 365 355 339 335
## [73,] 365 380 389 392 392 391 390 379 373 369
## [74,] 375 391 399 404 408 411 411 404 397 391
## [75,] 396 405 411 416 422 430 433 425 419 417
## [76,] 420 426 426 426 438 445 452 456 448 435
## [77,] 431 437 440 446 454 463 477 485 478 463
## [78,] 443 450 454 462 470 478 487 488 487 487
## [79,] 454 462 469 475 483 489 493 492 491 487
## [80,] 463 473 480 487 489 495 501 500 501 496
## [81,] 471 479 487 486 494 501 509 514 517 515
## [82,] 477 483 487 487 499 508 520 530 535 538
## [83,] 482 487 490 487 503 513 527 540 548 548
## [,478] [,479] [,480] [,481] [,482] [,483] [,484] [,485] [,486] [,487]
## [1,] 58 56 59 67 76 84 90 92 89 84
## [2,] 59 55 58 65 72 79 85 87 84 79
## [3,] 61 56 59 63 70 77 82 84 79 72
## [4,] 69 61 60 62 66 70 75 77 74 68
## [5,] 80 70 64 63 63 65 68 70 67 64
## [6,] 100 84 72 67 64 63 63 64 63 62
## [7,] 110 98 83 73 66 62 61 61 61 60
## [8,] 111 103 87 76 68 63 61 60 60 60
## [9,] 87 88 77 70 65 62 60 60 60 60
## [10,] 71 72 72 69 66 63 61 60 60 60
## [11,] 84 81 85 78 72 67 62 60 60 60
## [12,] 105 103 101 101 88 75 63 60 60 60
## [13,] 126 123 122 121 113 89 66 60 60 60
## [14,] 138 130 123 121 103 91 60 61 60 60
## [15,] 148 135 121 121 110 95 75 60 60 60
## [16,] 161 147 135 121 121 110 89 69 60 60
## [17,] 177 164 152 141 130 123 99 74 60 60
## [18,] 201 182 170 153 139 129 113 87 67 60
## [19,] 208 188 182 158 143 132 123 107 79 68
## [20,] 192 179 164 154 144 134 124 108 81 69
## [21,] 179 166 156 145 137 131 122 96 75 68
## [22,] 167 153 139 128 129 124 111 71 63 61
## [23,] 159 141 121 125 121 108 81 60 60 61
## [24,] 152 138 130 123 122 82 62 62 61 60
## [25,] 147 138 128 121 100 73 60 61 60 60
## [26,] 139 131 124 112 94 70 62 61 60 60
## [27,] 128 121 108 94 78 62 60 62 60 60
## [28,] 121 108 96 84 71 60 61 60 60 60
## [29,] 102 90 78 66 62 62 60 60 60 60
## [30,] 85 72 60 63 60 61 61 60 60 60
## [31,] 63 61 62 61 61 61 61 60 60 60
## [32,] 60 62 61 60 64 62 61 60 60 60
## [33,] 60 60 61 68 67 66 63 60 64 69
## [34,] 81 81 82 82 79 73 69 71 73 74
## [35,] 111 111 103 94 89 83 78 79 82 80
## [36,] 121 121 121 103 98 91 86 88 90 87
## [37,] 121 121 112 109 105 99 95 96 98 96
## [38,] 134 121 121 116 112 107 104 105 106 106
## [39,] 158 146 130 121 117 112 110 110 111 114
## [40,] 182 174 156 134 121 119 118 118 119 121
## [41,] 182 182 182 145 121 121 121 121 121 123
## [42,] 182 182 163 148 121 121 121 121 121 127
## [43,] 182 182 167 154 142 121 121 121 121 132
## [44,] 182 182 178 172 175 143 128 121 133 138
## [45,] 182 182 182 182 182 182 161 152 150 146
## [46,] 198 192 182 182 182 182 182 176 163 154
## [47,] 214 209 196 182 182 182 182 182 182 170
## [48,] 236 234 219 205 186 182 182 182 182 177
## [49,] 243 243 243 228 203 182 182 182 182 172
## [50,] 243 243 243 243 216 207 192 182 182 171
## [51,] 243 243 243 239 235 234 219 204 189 178
## [52,] 243 243 243 243 243 243 243 228 210 195
## [53,] 243 243 243 243 243 243 243 243 227 212
## [54,] 243 243 243 243 243 243 243 243 243 227
## [55,] 243 243 243 243 243 243 243 243 243 240
## [56,] 243 243 243 243 243 243 243 243 243 243
## [57,] 243 243 243 243 243 243 243 243 243 243
## [58,] 243 243 243 243 243 243 243 243 243 243
## [59,] 243 243 243 243 243 243 243 243 243 224
## [60,] 243 243 243 243 243 243 243 243 243 225
## [61,] 243 243 243 243 243 243 243 243 243 229
## [62,] 243 243 243 243 243 243 243 243 243 235
## [63,] 243 243 243 243 243 243 243 243 243 243
## [64,] 243 243 243 243 243 243 243 243 243 243
## [65,] 243 243 243 243 243 243 243 243 243 250
## [66,] 243 243 243 247 247 247 247 248 253 257
## [67,] 243 243 243 261 261 258 257 259 262 265
## [68,] 243 252 264 277 272 268 266 268 270 273
## [69,] 270 273 282 293 282 277 276 277 278 281
## [70,] 290 293 299 303 288 283 282 283 284 285
## [71,] 304 304 304 305 296 292 291 291 292 293
## [72,] 325 321 311 305 304 301 299 299 298 298
## [73,] 356 340 327 309 304 304 303 302 302 302
## [74,] 377 365 346 315 304 304 304 304 304 304
## [75,] 402 387 373 336 304 304 304 309 310 307
## [76,] 426 411 395 372 304 304 328 321 323 315
## [77,] 444 431 418 389 371 335 355 354 353 336
## [78,] 462 442 426 404 387 383 379 380 373 355
## [79,] 474 455 437 417 404 401 400 403 399 387
## [80,] 487 473 465 436 422 420 420 426 426 426
## [81,] 500 487 487 460 426 426 426 487 457 441
## [82,] 529 534 513 496 475 472 487 490 495 470
## [83,] 548 551 548 524 503 487 512 528 548 497
## [,488] [,489] [,490] [,491] [,492] [,493] [,494] [,495] [,496] [,497]
## [1,] 80 80 88 99 112 126 141 156 169 178
## [2,] 75 77 89 103 115 127 141 158 175 186
## [3,] 67 75 92 110 117 128 144 168 189 200
## [4,] 65 73 87 101 113 125 142 160 176 188
## [5,] 62 69 85 100 113 127 141 155 168 179
## [6,] 61 70 85 100 113 124 136 149 162 172
## [7,] 61 71 87 101 112 119 127 137 149 159
## [8,] 61 71 87 100 109 111 113 122 133 144
## [9,] 60 60 74 93 108 101 98 104 116 128
## [10,] 60 60 66 79 83 73 76 85 100 113
## [11,] 60 60 61 66 73 67 65 71 82 99
## [12,] 60 60 60 60 60 61 60 60 74 84
## [13,] 60 60 60 60 60 60 60 60 64 70
## [14,] 60 60 60 60 60 60 60 60 60 61
## [15,] 60 60 60 60 60 60 60 60 60 60
## [16,] 60 60 60 60 60 60 60 60 60 60
## [17,] 60 60 60 60 60 60 60 60 60 60
## [18,] 60 60 60 60 60 60 60 60 60 60
## [19,] 60 60 60 60 60 60 60 60 60 60
## [20,] 64 61 60 60 60 60 60 60 60 60
## [21,] 63 60 60 60 60 60 60 60 60 60
## [22,] 60 60 60 60 60 60 60 60 60 60
## [23,] 60 60 60 60 60 60 60 60 60 72
## [24,] 60 60 60 60 60 60 60 63 75 91
## [25,] 60 60 60 60 60 60 60 69 97 121
## [26,] 60 60 60 60 60 60 60 68 102 120
## [27,] 60 60 60 60 60 60 60 69 95 121
## [28,] 60 60 60 60 60 60 60 60 90 110
## [29,] 60 60 60 60 60 60 60 60 83 105
## [30,] 60 60 60 60 60 60 60 60 81 103
## [31,] 62 62 61 60 60 60 60 63 89 114
## [32,] 64 64 62 61 60 60 60 60 101 117
## [33,] 67 66 64 62 60 60 60 60 67 111
## [34,] 72 70 67 64 62 60 60 60 60 93
## [35,] 77 73 69 67 64 60 60 60 67 97
## [36,] 84 80 75 72 68 60 60 60 80 103
## [37,] 93 89 86 84 82 77 74 83 94 109
## [38,] 104 101 99 98 99 97 101 107 114 152
## [39,] 112 110 109 110 111 112 113 121 152 192
## [40,] 120 118 118 119 121 121 131 171 182 208
## [41,] 122 121 121 121 121 121 121 148 182 203
## [42,] 126 123 121 121 121 121 121 131 170 188
## [43,] 131 126 122 121 121 121 126 141 163 182
## [44,] 135 128 122 122 121 123 131 141 161 182
## [45,] 140 129 122 121 121 125 132 140 158 178
## [46,] 144 129 122 121 121 124 126 126 165 190
## [47,] 153 134 121 122 121 121 121 131 182 202
## [48,] 162 140 124 121 121 121 121 121 182 202
## [49,] 160 143 126 121 121 121 121 132 153 172
## [50,] 160 139 121 123 121 121 121 126 144 153
## [51,] 165 144 122 121 122 121 121 121 127 130
## [52,] 182 180 182 152 142 131 121 121 121 121
## [53,] 198 186 183 182 173 158 136 123 121 117
## [54,] 211 193 183 182 182 182 147 129 121 113
## [55,] 221 193 182 180 178 162 148 131 122 112
## [56,] 216 182 178 175 167 156 143 126 122 105
## [57,] 217 182 174 168 159 149 127 122 121 111
## [58,] 197 182 176 170 164 161 150 121 121 121
## [59,] 197 182 182 180 178 182 182 182 182 152
## [60,] 205 188 182 182 190 197 201 205 196 187
## [61,] 214 203 201 204 209 217 220 227 217 206
## [62,] 226 219 221 225 229 236 239 248 237 225
## [63,] 239 237 237 243 243 252 263 268 255 243
## [64,] 245 247 249 255 265 273 284 295 280 262
## [65,] 252 256 263 272 280 290 304 302 304 279
## [66,] 259 267 274 282 290 300 304 304 298 287
## [67,] 267 275 283 290 297 300 304 304 293 283
## [68,] 275 282 289 295 300 302 303 304 294 286
## [69,] 282 288 294 299 302 303 304 304 297 291
## [70,] 287 292 296 300 303 304 304 304 300 296
## [71,] 294 296 299 303 305 304 304 304 304 303
## [72,] 299 301 304 303 313 324 308 304 304 304
## [73,] 302 302 304 304 329 354 328 304 304 304
## [74,] 303 303 304 304 338 365 355 325 304 304
## [75,] 304 304 304 331 355 370 378 355 335 314
## [76,] 304 304 304 335 365 389 418 393 365 345
## [77,] 312 304 304 336 365 396 427 429 411 380
## [78,] 332 304 331 341 365 397 434 448 437 426
## [79,] 372 356 353 359 365 402 443 477 462 448
## [80,] 404 399 387 377 365 426 469 483 487 472
## [81,] 426 426 409 401 410 426 473 494 491 487
## [82,] 453 444 438 436 440 451 477 506 512 518
## [83,] 474 470 468 467 471 476 502 523 536 548
## [,498] [,499] [,500] [,501] [,502] [,503] [,504] [,505] [,506] [,507]
## [1,] 183 180 172 160 146 133 119 106 94 84
## [2,] 189 184 175 162 146 128 111 98 88 80
## [3,] 194 187 174 156 139 115 98 87 80 74
## [4,] 189 177 163 144 123 103 89 80 74 70
## [5,] 183 179 166 148 129 108 90 79 72 67
## [6,] 177 179 173 161 142 120 99 84 74 68
## [7,] 167 172 171 163 151 132 112 94 80 71
## [8,] 156 160 161 155 146 130 111 93 79 70
## [9,] 139 146 147 142 137 125 100 80 70 65
## [10,] 124 126 126 122 121 116 98 79 69 64
## [11,] 110 109 105 101 103 106 94 81 69 63
## [12,] 96 92 85 77 79 93 90 80 68 60
## [13,] 75 73 66 62 60 68 69 67 62 62
## [14,] 62 60 62 60 61 60 61 60 60 61
## [15,] 60 60 60 60 60 60 60 60 60 60
## [16,] 60 60 60 60 60 60 60 60 60 60
## [17,] 60 60 60 60 60 60 60 60 60 60
## [18,] 60 60 60 60 60 60 60 60 60 60
## [19,] 60 60 60 60 60 60 60 60 60 60
## [20,] 60 60 60 60 60 60 60 60 60 60
## [21,] 60 60 60 60 60 60 60 60 60 60
## [22,] 60 60 60 60 60 60 60 60 60 60
## [23,] 68 60 60 60 60 60 60 60 60 60
## [24,] 94 81 77 70 74 69 64 60 60 60
## [25,] 121 105 119 97 117 94 81 69 60 60
## [26,] 128 142 166 116 148 109 94 81 68 60
## [27,] 142 182 176 182 172 139 114 97 77 60
## [28,] 121 148 182 180 182 149 126 121 91 73
## [29,] 114 121 149 182 165 145 125 116 99 78
## [30,] 113 118 121 136 154 131 124 108 94 79
## [31,] 118 120 140 142 147 140 121 112 97 82
## [32,] 127 145 162 182 182 155 133 121 106 92
## [33,] 127 144 167 180 181 177 147 128 118 104
## [34,] 110 121 121 152 182 182 164 142 121 115
## [35,] 110 118 121 121 182 182 171 156 145 129
## [36,] 114 121 121 121 182 187 182 170 166 151
## [37,] 121 182 182 182 206 205 197 182 182 167
## [38,] 192 220 228 231 238 235 231 217 202 189
## [39,] 243 233 249 251 252 263 255 243 227 212
## [40,] 235 243 261 277 292 294 291 271 252 236
## [41,] 223 243 273 304 302 304 304 304 277 243
## [42,] 218 243 267 294 304 304 304 304 304 268
## [43,] 210 243 255 279 304 304 304 304 280 267
## [44,] 199 224 243 261 290 304 296 282 268 249
## [45,] 182 221 236 243 276 280 277 265 254 243
## [46,] 212 233 243 251 265 264 256 249 234 215
## [47,] 228 243 249 252 273 252 243 230 216 200
## [48,] 243 241 243 245 245 243 228 218 206 193
## [49,] 196 224 228 228 220 209 207 199 188 178
## [50,] 166 182 182 182 182 182 188 182 172 164
## [51,] 145 151 154 152 155 168 171 162 156 150
## [52,] 121 128 129 121 128 147 146 143 141 136
## [53,] 112 109 103 105 115 128 130 127 126 125
## [54,] 94 76 60 82 107 121 121 82 60 60
## [55,] 89 60 63 61 60 60 60 60 63 61
## [56,] 90 79 60 60 60 60 60 60 60 60
## [57,] 104 92 82 68 60 60 60 60 60 60
## [58,] 121 109 104 83 60 60 60 60 60 60
## [59,] 134 121 121 98 75 60 60 60 60 60
## [60,] 171 156 141 121 98 88 83 82 83 85
## [61,] 194 182 167 142 121 108 103 104 106 111
## [62,] 213 200 188 163 132 121 118 116 117 120
## [63,] 231 219 206 188 162 149 121 121 121 121
## [64,] 249 237 225 208 195 189 185 167 142 128
## [65,] 263 251 243 228 224 210 197 182 170 153
## [66,] 272 259 250 248 245 235 220 205 190 175
## [67,] 275 267 263 261 257 250 243 228 213 203
## [68,] 280 275 274 274 271 266 259 243 228 216
## [69,] 288 285 287 287 285 281 277 263 250 236
## [70,] 294 293 295 295 294 293 290 287 271 249
## [71,] 302 302 304 305 309 311 310 307 295 263
## [72,] 304 304 304 306 322 332 326 318 310 288
## [73,] 304 304 304 309 340 357 344 333 322 304
## [74,] 304 304 304 304 365 359 365 352 340 327
## [75,] 304 304 304 304 365 365 370 370 359 355
## [76,] 324 304 304 304 365 365 382 390 398 391
## [77,] 355 335 322 327 345 365 400 419 434 427
## [78,] 395 365 365 353 353 365 426 442 467 474
## [79,] 435 415 392 363 360 365 426 457 487 485
## [80,] 464 452 405 375 364 385 426 458 487 500
## [81,] 487 487 441 406 410 426 441 462 487 520
## [82,] 518 511 496 457 423 439 461 479 505 544
## [83,] 548 548 523 500 487 467 487 521 548 561
## [,508] [,509] [,510] [,511] [,512] [,513] [,514] [,515] [,516] [,517]
## [1,] 76 68 63 59 57 57 58 60 63 69
## [2,] 72 66 61 58 57 58 60 62 64 68
## [3,] 68 63 59 57 58 60 61 62 63 68
## [4,] 65 61 58 57 58 60 60 61 63 66
## [5,] 63 61 59 58 59 60 60 61 63 67
## [6,] 63 61 60 59 60 60 60 62 66 72
## [7,] 64 61 61 60 60 60 60 64 71 80
## [8,] 64 61 61 60 60 60 61 66 77 89
## [9,] 62 61 61 60 60 60 62 65 79 100
## [10,] 62 62 61 60 60 60 60 61 73 97
## [11,] 61 61 61 60 60 60 60 60 64 80
## [12,] 60 60 60 60 60 60 60 60 60 65
## [13,] 61 60 60 60 60 60 60 60 60 60
## [14,] 60 60 60 60 60 60 60 60 60 60
## [15,] 60 60 60 60 60 60 60 60 60 60
## [16,] 60 60 60 60 60 60 60 60 60 60
## [17,] 60 60 60 60 60 60 60 60 60 60
## [18,] 60 60 60 60 60 60 60 60 60 60
## [19,] 60 60 60 60 60 60 60 60 60 60
## [20,] 60 60 60 60 60 60 60 60 60 60
## [21,] 60 60 60 60 60 60 60 60 60 60
## [22,] 60 60 60 60 60 60 60 60 60 60
## [23,] 60 60 60 60 60 60 60 60 60 60
## [24,] 60 60 60 60 60 60 60 60 60 60
## [25,] 60 60 60 60 60 60 60 60 60 60
## [26,] 60 60 60 60 60 60 60 60 60 60
## [27,] 60 60 60 60 60 60 60 60 60 60
## [28,] 60 60 60 60 60 60 60 60 60 60
## [29,] 60 60 60 60 60 60 60 60 60 60
## [30,] 60 60 60 60 60 60 60 60 60 60
## [31,] 67 60 60 60 60 60 60 60 60 60
## [32,] 80 65 60 60 60 60 60 60 60 60
## [33,] 92 76 60 60 60 60 60 60 60 60
## [34,] 104 87 72 60 60 60 60 60 60 60
## [35,] 117 102 89 81 73 67 63 60 60 60
## [36,] 137 116 108 104 98 84 68 62 60 60
## [37,] 152 129 121 121 110 90 71 62 61 60
## [38,] 175 154 135 126 121 94 65 62 60 60
## [39,] 194 175 148 133 121 100 79 61 60 60
## [40,] 208 180 157 138 125 115 85 63 60 60
## [41,] 223 176 156 143 128 121 90 65 60 60
## [42,] 243 177 155 138 121 104 87 64 61 61
## [43,] 243 197 158 139 121 106 89 67 60 60
## [44,] 233 194 161 140 121 105 90 68 60 60
## [45,] 209 179 158 140 121 104 87 67 60 60
## [46,] 192 171 151 137 121 99 83 65 60 60
## [47,] 182 162 144 130 121 90 67 61 61 60
## [48,] 182 158 138 121 108 88 60 61 60 60
## [49,] 163 146 134 124 115 79 60 61 60 60
## [50,] 153 141 133 125 121 60 69 62 60 60
## [51,] 141 132 125 91 68 70 66 63 60 68
## [52,] 129 121 60 74 64 68 64 62 73 85
## [53,] 91 67 67 62 64 63 63 61 85 102
## [54,] 69 61 62 61 61 61 61 73 101 121
## [55,] 61 61 61 61 61 61 63 90 121 131
## [56,] 60 60 61 60 60 60 69 93 121 136
## [57,] 60 60 60 60 60 60 60 92 121 135
## [58,] 60 60 60 60 60 60 60 87 121 130
## [59,] 60 60 60 60 60 60 60 77 113 121
## [60,] 86 73 64 60 60 60 60 80 121 119
## [61,] 112 90 76 60 60 60 60 89 105 121
## [62,] 120 113 96 78 60 60 65 87 103 115
## [63,] 121 122 121 101 78 60 81 99 109 121
## [64,] 123 125 123 121 97 97 100 115 120 119
## [65,] 144 133 128 121 111 112 114 121 121 121
## [66,] 169 151 139 129 121 119 118 119 121 123
## [67,] 186 170 153 139 129 121 121 121 121 130
## [68,] 196 182 162 146 134 125 121 121 121 138
## [69,] 209 182 168 153 138 123 122 121 131 157
## [70,] 210 182 168 155 140 121 121 121 121 182
## [71,] 233 182 172 163 153 132 121 121 121 182
## [72,] 243 223 182 182 182 162 149 121 155 159
## [73,] 276 254 233 228 208 195 189 172 170 178
## [74,] 304 284 279 256 243 226 212 205 203 192
## [75,] 348 323 311 293 272 253 236 234 233 218
## [76,] 377 365 344 329 304 284 272 260 252 243
## [77,] 414 393 378 370 349 335 305 284 278 263
## [78,] 439 426 409 395 385 372 348 304 304 285
## [79,] 466 444 426 411 400 386 370 341 324 304
## [80,] 494 477 456 435 420 403 386 372 368 348
## [81,] 523 505 487 460 426 412 396 389 382 372
## [82,] 550 537 517 497 472 431 411 404 399 386
## [83,] 562 556 548 528 507 472 426 426 426 406
## [,518] [,519] [,520] [,521] [,522] [,523] [,524] [,525] [,526] [,527]
## [1,] 76 86 96 106 116 120 116 110 101 92
## [2,] 74 82 94 107 118 124 123 118 109 100
## [3,] 70 78 95 114 124 129 129 124 114 103
## [4,] 70 79 97 113 124 132 133 128 118 107
## [5,] 72 84 100 115 127 135 138 135 126 117
## [6,] 80 91 103 116 130 140 145 145 138 131
## [7,] 89 98 106 119 134 145 152 153 150 146
## [8,] 99 107 112 122 135 149 156 161 159 158
## [9,] 112 115 117 119 125 139 154 168 167 167
## [10,] 111 115 117 117 120 127 129 140 152 156
## [11,] 97 107 111 108 113 121 124 120 122 134
## [12,] 83 94 95 96 101 121 121 97 91 101
## [13,] 66 72 72 66 62 78 81 71 64 65
## [14,] 60 60 62 60 60 61 60 63 60 62
## [15,] 60 60 60 61 60 60 60 60 61 60
## [16,] 60 60 60 60 60 60 60 60 60 60
## [17,] 60 60 60 60 60 60 60 60 60 60
## [18,] 60 60 60 60 60 60 60 60 60 60
## [19,] 60 60 60 60 60 60 60 60 60 60
## [20,] 60 60 60 60 60 60 60 60 60 60
## [21,] 60 60 60 60 60 60 60 60 60 60
## [22,] 60 60 60 60 60 60 60 60 60 60
## [23,] 60 60 60 60 60 60 60 60 60 60
## [24,] 60 60 60 60 60 60 60 60 60 60
## [25,] 60 60 60 60 60 60 60 60 60 60
## [26,] 60 60 60 60 60 60 60 60 60 60
## [27,] 60 60 60 60 60 60 60 60 60 60
## [28,] 60 60 60 60 60 60 60 60 60 60
## [29,] 60 60 60 60 60 60 60 60 60 60
## [30,] 60 60 60 60 60 60 60 60 60 60
## [31,] 60 60 60 60 60 60 60 60 60 60
## [32,] 60 60 60 60 60 60 60 60 60 60
## [33,] 60 60 60 60 60 60 60 60 60 60
## [34,] 60 60 60 60 60 60 60 60 60 60
## [35,] 60 60 60 60 60 60 60 60 60 60
## [36,] 60 60 60 60 60 60 60 60 60 60
## [37,] 60 60 60 60 60 60 60 60 60 60
## [38,] 60 60 60 60 60 60 60 60 60 60
## [39,] 60 60 60 60 60 60 60 60 60 60
## [40,] 60 60 60 60 60 60 60 60 60 60
## [41,] 60 60 60 60 60 60 60 60 60 60
## [42,] 60 60 60 60 60 60 60 60 60 60
## [43,] 60 60 60 60 60 60 60 60 60 60
## [44,] 60 60 60 60 60 60 60 60 60 60
## [45,] 60 60 60 60 60 60 60 60 60 60
## [46,] 60 60 60 60 60 60 60 60 60 60
## [47,] 60 60 60 60 60 60 60 60 60 60
## [48,] 60 60 60 60 60 60 60 60 60 60
## [49,] 60 60 60 60 60 60 60 60 60 60
## [50,] 60 71 74 75 72 60 60 60 60 60
## [51,] 80 88 97 98 94 81 67 60 60 60
## [52,] 98 109 121 121 121 105 90 75 60 60
## [53,] 115 128 142 161 162 135 114 98 94 92
## [54,] 132 149 167 180 182 182 151 121 121 121
## [55,] 145 161 182 181 182 182 182 182 167 133
## [56,] 150 163 182 182 182 182 182 182 148 137
## [57,] 148 162 182 182 162 152 152 145 145 130
## [58,] 138 147 156 155 131 116 110 106 101 91
## [59,] 124 127 130 126 108 91 77 60 60 65
## [60,] 120 121 122 122 87 68 63 63 61 60
## [61,] 121 121 121 106 60 69 61 60 60 60
## [62,] 121 121 121 103 60 61 62 61 60 60
## [63,] 119 121 121 71 64 61 61 60 60 60
## [64,] 120 121 93 66 62 61 61 60 60 60
## [65,] 121 114 98 77 60 61 60 60 61 60
## [66,] 121 113 103 83 60 60 60 60 65 60
## [67,] 130 121 111 93 75 60 60 72 75 67
## [68,] 143 136 121 103 85 78 78 80 85 80
## [69,] 172 170 150 123 103 95 96 97 99 95
## [70,] 178 182 182 151 121 111 111 112 112 111
## [71,] 182 182 188 176 152 139 132 129 126 124
## [72,] 182 182 201 197 182 182 165 151 141 131
## [73,] 181 182 224 231 213 196 182 169 152 136
## [74,] 182 214 241 243 243 222 189 182 160 139
## [75,] 218 223 238 242 243 243 182 165 146 128
## [76,] 236 235 240 243 243 243 199 156 121 121
## [77,] 249 242 242 243 243 243 192 166 145 116
## [78,] 266 243 243 245 243 219 193 177 162 136
## [79,] 284 264 247 248 243 231 214 198 182 154
## [80,] 319 294 277 262 253 246 235 215 193 170
## [81,] 365 329 299 277 264 253 247 243 223 190
## [82,] 371 358 315 288 272 258 248 244 222 189
## [83,] 385 365 321 291 275 257 243 220 201 192
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## [2,] 90 80 72 67 63 59 55 53 51 50
## [3,] 92 83 76 71 67 63 60 58 56 55
## [4,] 95 88 81 75 69 65 62 60 58 57
## [5,] 107 97 88 81 74 70 66 64 62 60
## [6,] 122 112 101 91 85 79 74 72 69 66
## [7,] 139 132 122 110 99 91 85 83 79 75
## [8,] 156 153 142 130 119 108 98 94 90 85
## [9,] 173 175 164 149 137 123 112 106 102 96
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## [12,] 121 121 121 121 121 122 123 122 122 121
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## [18,] 60 60 60 60 60 60 61 60 60 61
## [19,] 60 60 60 60 60 60 63 60 60 60
## [20,] 60 60 60 60 60 60 74 76 64 60
## [21,] 60 60 60 60 60 79 91 101 84 60
## [22,] 60 60 60 60 79 98 114 119 103 66
## [23,] 60 60 60 60 89 121 115 121 103 72
## [24,] 60 60 60 60 86 121 121 121 88 70
## [25,] 60 60 60 65 71 79 91 92 76 64
## [26,] 60 60 60 60 60 60 62 60 62 60
## [27,] 60 60 60 60 60 60 60 60 60 60
## [28,] 60 60 60 60 60 60 60 60 60 60
## [29,] 60 60 60 60 60 60 60 60 60 60
## [30,] 60 60 60 60 60 60 60 60 60 60
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## [40,] 60 60 60 60 60 60 60 60 60 60
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## [44,] 60 60 60 60 60 60 60 60 60 60
## [45,] 60 60 60 60 60 60 60 60 60 60
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## [49,] 60 60 60 60 60 60 60 60 60 60
## [50,] 60 60 60 60 60 60 60 60 60 60
## [51,] 60 60 60 60 60 60 60 60 60 60
## [52,] 60 60 60 60 60 60 60 60 60 60
## [53,] 91 91 84 73 65 60 60 60 60 60
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## [56,] 123 121 121 121 121 121 93 60 60 60
## [57,] 121 121 121 121 121 121 71 63 61 60
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## [59,] 60 60 60 60 60 60 60 60 60 60
## [60,] 60 60 60 60 60 60 60 60 60 60
## [61,] 60 60 60 60 60 60 60 60 60 60
## [62,] 60 60 60 60 60 60 60 60 60 60
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## [66,] 60 60 60 60 60 60 60 60 60 60
## [67,] 60 60 60 62 61 60 60 60 60 60
## [68,] 70 60 71 68 66 63 60 60 60 60
## [69,] 88 86 81 78 73 68 60 60 60 60
## [70,] 107 102 97 93 86 81 67 60 60 60
## [71,] 122 117 115 114 104 100 91 73 69 65
## [72,] 124 122 121 121 121 121 121 104 94 86
## [73,] 126 123 122 121 103 118 121 121 115 113
## [74,] 127 123 121 121 81 116 121 122 125 128
## [75,] 123 102 76 71 60 119 121 124 130 138
## [76,] 91 60 66 61 60 91 121 126 138 149
## [77,] 91 60 60 63 61 71 121 128 140 156
## [78,] 109 77 60 60 60 60 74 121 137 160
## [79,] 131 121 81 60 60 60 60 101 121 155
## [80,] 139 121 91 60 60 60 74 121 133 146
## [81,] 148 121 94 60 60 60 81 121 129 136
## [82,] 162 133 111 60 60 60 60 84 110 123
## [83,] 182 157 121 101 60 60 60 60 79 100
## [,538] [,539] [,540] [,541] [,542] [,543] [,544] [,545] [,546] [,547]
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## [2,] 49 49 49 49 48 47 45 43 41 40
## [3,] 53 52 51 50 50 49 46 45 44 43
## [4,] 55 54 52 51 51 49 47 46 45 45
## [5,] 58 56 54 53 53 50 48 48 47 46
## [6,] 62 59 57 56 55 52 50 50 49 48
## [7,] 69 64 61 59 57 54 52 52 52 50
## [8,] 78 71 66 63 60 57 55 54 54 52
## [9,] 86 78 72 69 65 61 58 57 56 54
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## [20,] 60 60 60 60 60 61 61 60 65 68
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## [29,] 60 60 60 60 60 60 60 60 60 60
## [30,] 60 60 60 60 60 60 60 60 60 60
## [31,] 60 60 60 60 60 60 60 60 60 60
## [32,] 60 60 60 60 60 60 60 60 60 60
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## [34,] 61 63 62 60 60 62 60 60 60 60
## [35,] 62 65 67 69 72 70 65 60 60 60
## [36,] 64 70 74 80 88 89 80 69 60 60
## [37,] 66 75 84 93 112 121 104 98 79 60
## [38,] 65 74 84 92 108 121 121 121 111 109
## [39,] 67 74 78 84 92 110 121 121 121 121
## [40,] 62 65 68 70 74 98 112 121 121 121
## [41,] 60 60 61 60 61 88 108 121 121 121
## [42,] 60 60 60 60 65 87 116 119 121 121
## [43,] 60 60 60 60 68 89 98 121 121 121
## [44,] 60 60 60 60 69 77 83 93 112 121
## [45,] 60 60 60 60 60 62 61 69 88 101
## [46,] 60 60 60 60 60 60 60 60 70 77
## [47,] 60 60 60 60 60 60 60 60 60 60
## [48,] 60 60 60 60 60 60 60 60 60 60
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## [50,] 60 60 60 60 60 60 60 60 60 60
## [51,] 60 60 60 60 60 60 60 60 60 60
## [52,] 60 60 60 60 60 60 60 60 60 60
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## [70,] 60 60 60 60 60 60 60 60 60 64
## [71,] 60 67 65 60 60 60 60 60 60 73
## [72,] 89 83 77 66 60 60 60 60 60 85
## [73,] 113 102 92 78 67 60 60 70 83 99
## [74,] 126 121 114 96 88 85 87 92 103 113
## [75,] 142 146 139 115 113 112 106 108 116 118
## [76,] 161 171 182 182 182 182 137 129 124 121
## [77,] 171 182 197 213 213 188 182 154 134 123
## [78,] 182 182 220 243 225 201 182 165 139 121
## [79,] 182 192 201 202 182 182 174 160 139 121
## [80,] 159 171 173 171 166 156 151 143 130 112
## [81,] 142 145 144 144 141 136 131 121 113 90
## [82,] 125 127 121 126 125 107 101 77 81 68
## [83,] 121 122 101 60 60 60 60 67 60 63
## [,548] [,549] [,550] [,551] [,552] [,553] [,554] [,555] [,556] [,557]
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## [2,] 38 36 35 34 33 33 33 33 33 33
## [3,] 41 39 38 37 36 35 36 37 37 37
## [4,] 43 41 39 39 38 37 38 39 39 39
## [5,] 44 42 41 41 39 39 40 40 40 41
## [6,] 45 44 43 43 41 42 42 42 43 43
## [7,] 47 46 45 45 43 44 44 45 45 45
## [8,] 49 48 47 47 45 46 46 47 47 47
## [9,] 51 50 49 49 47 48 49 49 49 49
## [10,] 53 52 51 51 49 50 51 51 51 51
## [11,] 55 54 53 53 51 52 52 53 53 53
## [12,] 56 56 55 55 53 54 54 55 55 55
## [13,] 58 58 57 56 56 56 56 57 57 57
## [14,] 60 60 59 59 58 58 58 59 59 60
## [15,] 60 61 60 60 60 60 60 63 60 70
## [16,] 64 64 62 60 60 60 69 74 75 87
## [17,] 66 68 68 66 60 75 85 92 100 111
## [18,] 69 74 76 77 82 91 101 108 119 126
## [19,] 73 80 86 91 97 110 121 121 121 141
## [20,] 71 77 83 88 94 103 106 115 124 140
## [21,] 63 66 68 69 68 60 60 83 119 137
## [22,] 60 62 63 63 60 62 60 60 123 132
## [23,] 60 60 61 60 61 60 60 80 108 125
## [24,] 60 60 60 60 60 60 60 70 88 121
## [25,] 60 60 60 60 60 60 60 60 63 62
## [26,] 60 60 60 60 60 60 60 60 60 60
## [27,] 60 60 60 60 60 60 60 60 60 60
## [28,] 60 60 60 60 60 60 60 60 60 60
## [29,] 60 60 60 60 60 60 60 60 60 60
## [30,] 60 60 60 60 60 60 60 60 60 60
## [31,] 60 60 60 60 60 60 60 60 60 60
## [32,] 60 60 60 60 60 60 60 60 60 60
## [33,] 60 60 60 60 60 60 60 60 60 60
## [34,] 60 61 60 60 60 60 60 60 60 60
## [35,] 66 73 60 60 60 60 60 60 60 60
## [36,] 77 108 94 74 65 62 60 60 60 60
## [37,] 111 114 121 89 75 67 62 60 60 60
## [38,] 119 119 121 94 76 68 62 61 60 60
## [39,] 120 121 94 81 60 65 60 60 60 60
## [40,] 121 110 83 66 64 61 61 60 60 60
## [41,] 118 96 68 65 64 60 60 60 60 60
## [42,] 118 98 73 60 60 61 60 60 60 60
## [43,] 121 121 101 82 60 60 60 60 60 60
## [44,] 121 121 121 101 88 73 60 60 60 60
## [45,] 118 121 121 121 113 110 80 68 60 64
## [46,] 97 121 121 121 121 88 86 85 89 81
## [47,] 70 86 98 99 72 85 93 112 113 112
## [48,] 60 60 66 60 60 71 90 106 121 121
## [49,] 60 60 60 61 61 64 72 90 100 109
## [50,] 60 60 60 60 60 60 60 72 77 79
## [51,] 60 60 60 60 60 60 60 60 60 60
## [52,] 60 60 60 60 60 60 60 60 60 60
## [53,] 60 60 60 60 60 60 60 60 60 60
## [54,] 60 60 60 60 60 60 60 60 60 60
## [55,] 60 60 60 60 60 60 60 60 60 60
## [56,] 60 60 60 60 60 60 60 60 60 60
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## [60,] 60 60 60 60 60 60 60 60 60 60
## [61,] 60 60 60 60 60 60 60 60 60 60
## [62,] 60 60 60 60 60 60 60 60 60 60
## [63,] 60 60 60 60 60 60 60 60 60 60
## [64,] 60 60 60 60 60 60 60 60 60 60
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## [68,] 60 60 60 60 60 60 60 60 60 60
## [69,] 60 60 60 60 60 60 60 60 60 60
## [70,] 60 60 60 60 60 60 60 60 60 60
## [71,] 76 68 60 60 60 60 60 60 60 60
## [72,] 101 96 76 60 60 60 60 60 60 60
## [73,] 121 121 107 71 60 60 60 60 60 60
## [74,] 121 121 121 90 71 61 61 60 60 60
## [75,] 118 121 100 90 70 61 61 60 60 60
## [76,] 121 103 88 67 62 62 61 60 60 60
## [77,] 121 99 79 60 60 61 61 60 60 60
## [78,] 105 92 76 63 60 60 60 60 60 60
## [79,] 102 85 69 60 61 60 60 60 60 60
## [80,] 94 75 60 61 60 60 60 60 60 60
## [81,] 74 60 63 60 60 60 60 60 60 60
## [82,] 62 62 61 61 60 60 60 60 60 60
## [83,] 60 61 60 60 60 60 60 60 60 60
## [,558] [,559] [,560] [,561] [,562] [,563] [,564] [,565] [,566] [,567]
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## [2,] 33 32 32 32 32 33 34 36 37 38
## [3,] 37 37 37 37 37 37 39 41 42 43
## [4,] 39 39 39 39 39 40 41 43 45 45
## [5,] 41 41 41 41 41 42 44 45 46 46
## [6,] 43 43 43 43 43 44 46 47 48 49
## [7,] 45 45 45 45 46 46 48 49 50 51
## [8,] 47 47 47 48 48 48 50 51 52 53
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## [10,] 51 52 52 52 53 53 54 55 56 57
## [11,] 53 53 53 54 54 55 56 56 57 58
## [12,] 55 55 56 56 56 56 57 57 58 58
## [13,] 57 58 58 58 58 58 58 59 59 59
## [14,] 60 63 60 59 59 59 59 59 59 60
## [15,] 80 76 69 60 60 60 60 60 60 60
## [16,] 100 99 89 82 80 71 63 60 60 60
## [17,] 121 121 109 100 98 91 78 67 60 60
## [18,] 132 142 133 116 115 111 97 80 66 60
## [19,] 156 182 182 152 151 182 121 96 82 71
## [20,] 154 166 182 176 175 164 121 105 91 79
## [21,] 147 157 168 182 174 148 134 117 103 91
## [22,] 140 146 158 163 160 145 133 121 114 102
## [23,] 126 128 140 145 140 131 128 125 122 115
## [24,] 103 111 121 126 124 121 124 123 122 121
## [25,] 72 79 79 91 107 118 121 122 122 122
## [26,] 61 60 62 60 71 112 121 121 121 121
## [27,] 60 60 60 60 60 115 119 121 121 121
## [28,] 60 60 60 60 68 87 121 119 121 121
## [29,] 60 60 60 60 60 70 75 91 111 121
## [30,] 60 60 60 60 60 60 60 60 60 77
## [31,] 60 60 60 60 60 60 60 60 60 60
## [32,] 60 60 60 60 60 60 60 60 60 60
## [33,] 60 60 60 60 60 60 60 60 60 60
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## [40,] 60 60 60 60 60 60 60 60 60 60
## [41,] 60 60 60 60 60 60 60 60 60 60
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## [43,] 60 60 60 60 60 60 60 60 60 60
## [44,] 60 60 60 60 60 60 60 60 60 60
## [45,] 60 60 60 60 60 60 60 60 60 60
## [46,] 74 60 60 60 60 60 60 60 60 61
## [47,] 109 84 60 60 60 60 60 60 60 66
## [48,] 121 121 77 60 60 60 60 60 72 78
## [49,] 110 80 73 64 60 60 60 79 88 97
## [50,] 84 70 65 63 63 60 83 95 106 117
## [51,] 66 66 63 62 65 83 97 121 121 120
## [52,] 60 60 60 63 70 83 97 109 121 121
## [53,] 60 60 60 64 74 81 92 105 121 121
## [54,] 60 60 60 63 65 74 83 92 102 118
## [55,] 60 60 60 60 60 60 71 77 82 86
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## [57,] 60 60 60 60 60 60 60 60 60 61
## [58,] 60 60 60 60 60 60 60 60 60 60
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## [60,] 60 60 60 60 60 60 60 60 60 60
## [61,] 60 60 60 60 60 60 60 60 60 60
## [62,] 60 60 60 60 60 60 60 60 60 60
## [63,] 60 60 60 60 60 60 60 60 60 60
## [64,] 60 60 60 60 60 60 60 60 60 60
## [65,] 60 60 60 60 60 60 60 60 60 60
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## [71,] 60 60 60 60 60 60 60 60 59 58
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## [82,] 60 60 60 60 60 60 60 60 58 55
## [83,] 60 60 60 60 60 60 60 60 58 55
## [,568] [,569] [,570] [,571] [,572] [,573] [,574] [,575] [,576] [,577]
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## [2,] 38 39 41 43 45 47 50 53 57 66
## [3,] 43 44 46 48 50 53 56 59 63 74
## [4,] 45 46 49 51 53 56 59 61 66 77
## [5,] 47 48 51 52 55 57 60 63 70 81
## [6,] 49 50 52 54 56 59 63 68 75 87
## [7,] 52 53 54 56 59 64 69 76 83 93
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## [13,] 60 66 106 121 119 121 121 134 154 165
## [14,] 60 60 91 111 121 121 121 125 141 151
## [15,] 60 60 60 60 60 121 91 110 126 136
## [16,] 60 60 60 60 68 64 60 81 101 124
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## [18,] 60 60 60 60 60 60 60 60 60 60
## [19,] 60 60 60 60 60 60 60 60 60 60
## [20,] 69 60 60 60 60 60 60 60 60 60
## [21,] 79 64 60 60 60 60 60 60 60 60
## [22,] 87 67 60 60 60 60 60 60 60 60
## [23,] 98 75 60 60 60 60 59 59 59 59
## [24,] 113 89 60 60 60 60 59 59 59 59
## [25,] 121 109 80 65 60 60 59 58 58 58
## [26,] 121 134 94 74 60 60 58 58 58 58
## [27,] 121 146 100 74 63 59 58 58 58 58
## [28,] 121 109 89 60 62 58 57 57 57 57
## [29,] 100 81 66 61 59 57 57 57 57 57
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## [37,] 60 58 55 51 48 48 47 46 44 42
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## [39,] 60 56 53 49 45 41 37 33 30 27
## [40,] 60 56 52 48 44 40 35 30 27 24
## [41,] 60 56 52 48 44 41 35 30 26 23
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## [43,] 60 56 52 49 45 42 37 32 29 26
## [44,] 60 56 53 49 46 43 39 35 32 29
## [45,] 60 57 53 50 47 45 41 38 35 32
## [46,] 60 57 54 52 49 47 45 42 39 35
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## [48,] 70 60 58 57 56 55 54 50 46 42
## [49,] 89 78 67 60 60 60 59 54 49 45
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## [51,] 121 115 113 110 92 79 67 60 53 49
## [52,] 121 121 121 121 114 96 72 60 55 53
## [53,] 117 121 121 121 121 109 71 60 57 56
## [54,] 103 98 113 121 117 107 76 63 59 59
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## [67,] 59 58 57 55 55 54 52 50 49 47
## [68,] 58 57 56 54 54 52 49 47 46 44
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## [70,] 58 56 55 53 51 48 45 42 40 38
## [71,] 57 56 55 52 49 46 42 40 38 35
## [72,] 57 55 54 51 49 44 41 38 36 33
## [73,] 56 55 53 51 48 44 40 38 35 32
## [74,] 56 54 53 50 48 44 40 37 35 32
## [75,] 56 54 53 50 47 43 39 37 35 32
## [76,] 55 53 52 49 47 43 39 37 35 32
## [77,] 55 53 51 49 45 42 40 37 35 33
## [78,] 54 52 51 49 46 42 40 38 36 34
## [79,] 54 52 50 49 46 43 41 39 37 35
## [80,] 53 52 50 48 46 43 41 39 37 36
## [81,] 53 52 50 48 46 43 41 39 38 36
## [82,] 54 52 50 48 46 43 41 40 38 36
## [83,] 54 52 50 49 46 43 42 40 38 36
## [,578] [,579] [,580] [,581] [,582] [,583] [,584] [,585] [,586] [,587]
## [1,] 69 81 94 108 123 136 147 157 162 165
## [2,] 77 90 106 124 141 156 167 175 179 180
## [3,] 86 101 120 141 162 179 186 192 195 195
## [4,] 90 105 122 141 161 181 197 206 209 208
## [5,] 94 109 125 144 166 189 207 217 218 216
## [6,] 101 115 132 151 173 195 212 221 220 216
## [7,] 105 119 136 157 179 200 214 219 215 207
## [8,] 114 126 141 161 182 201 211 214 205 194
## [9,] 124 134 146 160 176 197 219 215 198 175
## [10,] 143 155 163 171 175 180 187 171 153 140
## [11,] 166 169 174 178 165 161 157 153 138 128
## [12,] 182 182 179 182 151 139 131 129 125 112
## [13,] 176 182 182 182 131 120 113 110 102 92
## [14,] 157 166 166 147 119 107 100 93 84 76
## [15,] 140 145 141 133 114 95 85 77 69 60
## [16,] 126 128 128 125 106 80 67 64 62 62
## [17,] 121 122 122 121 91 60 64 61 60 61
## [18,] 76 110 121 111 88 68 60 62 61 60
## [19,] 72 83 87 92 76 60 63 61 61 60
## [20,] 60 75 72 73 66 63 61 61 60 60
## [21,] 60 60 63 62 61 60 60 60 60 60
## [22,] 60 60 60 60 60 60 60 60 60 60
## [23,] 59 59 60 59 59 59 59 59 59 59
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## [25,] 58 59 59 59 59 59 59 59 59 59
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## [29,] 57 57 57 57 58 58 58 58 59 59
## [30,] 57 57 57 57 57 57 58 58 58 58
## [31,] 56 56 56 57 57 57 57 57 57 57
## [32,] 56 56 56 56 56 56 56 56 56 56
## [33,] 55 55 54 54 54 54 54 54 54 54
## [34,] 53 53 52 52 51 51 50 50 50 50
## [35,] 50 50 49 48 46 46 45 44 44 44
## [36,] 46 45 44 42 39 37 36 35 35 35
## [37,] 41 39 37 34 29 27 25 25 26 26
## [38,] 33 31 28 23 16 14 13 15 15 16
## [39,] 24 21 17 10 0 0 0 5 6 6
## [40,] 21 17 13 4 1 0 0 0 0 0
## [41,] 19 16 12 6 2 0 0 0 0 0
## [42,] 20 17 13 8 6 4 2 0 0 0
## [43,] 23 19 16 12 10 8 6 3 1 0
## [44,] 25 22 19 16 14 12 10 7 5 1
## [45,] 29 26 23 19 17 16 14 12 9 5
## [46,] 32 29 26 23 21 20 18 16 14 10
## [47,] 35 32 30 27 25 24 23 21 18 14
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## [83,] 16 17 17 18 19 19 20 21 21 22
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## [2,] 27 28 29 30 30 30 30 30 30 30
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## [81,] 24 25 26 26 27 28 29 30 32 33
## [82,] 24 24 25 25 26 27 29 30 31 32
## [83,] 23 24 24 25 25 26 28 29 30 31
## [,798] [,799] [,800] [,801] [,802] [,803] [,804] [,805] [,806] [,807]
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## [2,] 30 31 32 33 33 34 34 34 34 35
## [3,] 36 38 39 40 40 41 41 41 41 42
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## [45,] 50 51 52 53 53 54 55 56 56 57
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## [52,] 49 50 51 52 53 55 57 58 60 60
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## [62,] 45 46 46 47 48 49 50 51 52 52
## [63,] 44 45 46 46 48 49 49 50 51 52
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## [72,] 40 41 42 43 44 45 46 47 48 49
## [73,] 40 41 42 42 44 45 46 47 48 49
## [74,] 39 40 41 42 43 44 45 46 47 48
## [75,] 39 39 40 41 42 44 45 46 46 47
## [76,] 38 39 39 41 42 43 44 45 46 47
## [77,] 37 38 39 40 41 42 43 44 45 46
## [78,] 36 37 38 40 41 42 43 44 45 46
## [79,] 35 36 37 39 40 41 42 43 44 45
## [80,] 35 35 36 38 39 40 41 42 43 44
## [81,] 34 35 35 37 38 39 40 41 42 43
## [82,] 33 34 35 36 37 38 39 40 41 42
## [83,] 32 33 34 35 37 38 39 40 41 42
## [,808] [,809] [,810] [,811] [,812] [,813] [,814] [,815] [,816] [,817]
## [1,] 27 28 29 30 31 32 32 33 33 34
## [2,] 36 37 38 39 39 40 40 41 41 42
## [3,] 43 44 45 46 46 46 47 47 47 48
## [4,] 47 48 49 50 50 49 50 50 50 51
## [5,] 49 50 50 51 51 50 51 51 51 51
## [6,] 49 51 51 51 51 50 51 52 52 52
## [7,] 50 51 52 52 52 51 52 53 53 53
## [8,] 51 52 52 52 52 52 53 53 54 54
## [9,] 52 52 53 53 53 53 54 54 54 55
## [10,] 52 53 53 53 54 54 55 55 55 56
## [11,] 53 53 53 54 54 54 55 56 56 56
## [12,] 53 53 54 54 55 55 56 56 57 57
## [13,] 54 54 55 55 56 56 57 57 58 58
## [14,] 55 55 56 56 56 57 58 58 58 59
## [15,] 56 56 57 57 58 58 59 59 59 60
## [16,] 57 58 58 58 59 60 60 60 60 60
## [17,] 58 58 59 59 60 60 60 60 60 60
## [18,] 59 59 59 60 60 60 60 60 60 60
## [19,] 59 59 59 60 60 60 60 60 60 60
## [20,] 60 60 60 60 60 60 60 60 60 60
## [21,] 60 60 60 60 60 60 60 60 60 60
## [22,] 60 60 60 60 60 60 60 60 60 60
## [23,] 60 60 60 60 60 60 60 60 60 60
## [24,] 60 60 60 60 60 60 60 60 60 60
## [25,] 60 60 60 60 60 60 60 60 60 60
## [26,] 60 60 60 60 60 60 60 60 60 60
## [27,] 60 60 60 60 60 60 60 60 60 60
## [28,] 60 60 60 60 60 60 60 60 60 60
## [29,] 60 60 60 60 60 60 60 60 60 60
## [30,] 60 60 60 60 60 60 60 60 60 60
## [31,] 60 60 60 60 60 60 60 60 60 60
## [32,] 60 60 60 60 60 60 60 60 60 60
## [33,] 60 60 60 60 60 60 60 60 60 60
## [34,] 60 60 60 60 60 60 60 60 60 60
## [35,] 60 60 60 60 60 60 60 60 60 60
## [36,] 60 60 60 60 60 60 60 60 60 60
## [37,] 60 60 60 60 60 60 60 60 60 60
## [38,] 60 60 60 60 60 60 60 60 60 60
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## [40,] 59 59 59 60 60 60 60 60 60 60
## [41,] 59 59 59 59 60 60 60 60 60 60
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## [44,] 58 58 59 59 60 60 60 60 60 60
## [45,] 57 58 59 59 60 60 60 60 60 60
## [46,] 57 58 59 59 60 60 60 60 60 60
## [47,] 57 58 59 60 60 60 60 60 60 60
## [48,] 58 59 60 63 64 64 65 67 72 68
## [49,] 59 60 64 69 73 76 79 83 85 83
## [50,] 61 62 70 78 84 89 94 97 98 98
## [51,] 63 67 78 88 96 103 110 111 113 113
## [52,] 65 72 85 98 108 117 120 121 121 121
## [53,] 68 75 88 103 121 120 121 121 121 121
## [54,] 63 71 86 98 107 121 121 121 121 121
## [55,] 60 65 78 83 89 88 102 113 121 121
## [56,] 59 60 64 66 66 60 76 84 109 121
## [57,] 58 59 60 60 60 61 60 60 68 100
## [58,] 57 58 59 59 59 59 60 60 60 60
## [59,] 56 57 58 58 58 59 59 59 60 60
## [60,] 55 56 57 57 58 58 59 59 60 60
## [61,] 54 55 56 57 57 58 59 59 60 60
## [62,] 53 54 55 56 57 58 59 59 60 60
## [63,] 52 54 55 56 56 57 58 59 60 60
## [64,] 52 53 55 56 56 57 58 59 60 60
## [65,] 52 53 55 56 56 57 58 60 60 60
## [66,] 52 53 54 55 56 57 58 59 60 60
## [67,] 51 53 54 55 56 56 57 58 60 60
## [68,] 51 52 53 54 55 56 57 58 59 60
## [69,] 51 52 53 54 54 55 56 58 59 60
## [70,] 50 51 52 53 54 55 56 57 58 59
## [71,] 50 51 52 53 54 55 56 57 58 59
## [72,] 50 51 52 53 54 55 56 57 59 60
## [73,] 50 51 52 53 54 55 56 58 60 60
## [74,] 49 51 52 53 54 55 56 57 59 60
## [75,] 49 50 51 52 53 54 55 57 58 59
## [76,] 48 50 51 52 53 53 55 56 58 58
## [77,] 48 49 50 51 52 53 54 56 57 58
## [78,] 47 48 49 50 51 52 53 55 56 57
## [79,] 46 47 48 49 50 51 53 54 55 56
## [80,] 45 46 47 48 49 50 52 53 54 55
## [81,] 44 46 47 48 49 50 51 53 54 55
## [82,] 44 45 46 47 48 49 51 52 53 54
## [83,] 43 45 46 47 48 49 50 52 53 54
## [,818] [,819] [,820] [,821] [,822] [,823] [,824] [,825] [,826] [,827]
## [1,] 35 36 37 38 39 40 42 45 49 52
## [2,] 42 43 43 44 45 46 48 50 52 55
## [3,] 48 48 48 48 49 50 52 54 56 58
## [4,] 51 51 50 50 51 51 53 55 57 59
## [5,] 52 52 51 52 52 52 55 56 57 60
## [6,] 52 53 52 53 53 53 56 57 58 60
## [7,] 53 53 53 54 54 54 56 57 58 60
## [8,] 54 54 54 55 55 55 57 58 58 60
## [9,] 55 55 56 56 56 57 57 58 59 60
## [10,] 56 56 57 58 57 58 58 59 60 60
## [11,] 57 58 59 59 59 59 59 60 60 60
## [12,] 58 59 60 60 60 60 60 60 60 60
## [13,] 59 60 60 60 60 60 60 60 60 60
## [14,] 59 60 60 60 60 60 60 60 60 60
## [15,] 60 60 60 60 60 60 60 60 60 60
## [16,] 60 60 60 60 60 60 60 60 60 60
## [17,] 60 60 60 60 60 60 60 60 60 60
## [18,] 60 60 60 60 60 60 60 60 60 60
## [19,] 60 60 60 60 60 60 60 60 60 60
## [20,] 60 60 60 60 60 60 60 60 60 60
## [21,] 60 60 60 60 60 60 60 60 60 60
## [22,] 60 60 60 60 60 60 60 60 60 60
## [23,] 60 60 60 60 60 60 60 60 60 60
## [24,] 60 60 60 60 60 60 60 60 60 60
## [25,] 60 60 60 60 60 60 60 60 60 60
## [26,] 60 60 60 60 60 60 60 60 60 60
## [27,] 60 60 60 60 60 60 60 60 60 60
## [28,] 60 60 60 60 60 60 60 60 60 60
## [29,] 60 60 60 60 60 60 60 60 60 60
## [30,] 60 60 60 60 60 60 60 60 60 60
## [31,] 60 60 60 60 60 60 60 60 60 60
## [32,] 60 60 60 60 60 60 60 60 60 60
## [33,] 60 60 60 60 60 60 60 60 60 60
## [34,] 60 60 60 60 60 60 60 60 60 60
## [35,] 60 60 60 60 60 60 60 60 60 60
## [36,] 60 60 60 60 60 60 60 60 60 60
## [37,] 60 60 60 60 60 60 60 60 60 60
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## [40,] 60 60 60 60 60 60 60 60 60 60
## [41,] 60 60 60 60 60 60 60 60 60 60
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## [43,] 60 60 60 60 60 60 60 60 60 60
## [44,] 60 60 60 60 60 60 60 60 60 60
## [45,] 60 60 60 60 60 60 60 60 60 60
## [46,] 60 60 60 60 60 60 60 60 60 60
## [47,] 60 60 60 60 60 60 60 64 60 71
## [48,] 63 60 66 69 69 68 78 78 84 88
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## [50,] 95 97 102 105 104 105 108 112 117 129
## [51,] 113 114 121 121 121 121 118 121 157 158
## [52,] 120 121 120 121 121 140 121 182 182 182
## [53,] 121 121 121 121 121 148 175 175 180 182
## [54,] 121 121 121 121 121 144 162 171 182 182
## [55,] 121 121 121 121 121 136 151 160 169 178
## [56,] 121 121 121 121 121 126 138 147 156 164
## [57,] 101 110 121 121 118 119 126 134 143 149
## [58,] 60 60 93 121 113 107 114 121 130 135
## [59,] 60 60 60 76 88 92 101 111 120 123
## [60,] 60 60 60 60 60 77 89 103 121 115
## [61,] 60 60 60 60 60 60 68 83 89 101
## [62,] 60 60 60 60 60 60 60 60 71 81
## [63,] 60 60 60 60 60 60 60 60 60 71
## [64,] 60 60 60 60 61 61 60 60 60 60
## [65,] 60 60 60 60 63 64 63 60 60 60
## [66,] 60 60 60 60 64 67 68 66 63 60
## [67,] 60 60 60 60 67 72 74 74 73 73
## [68,] 60 60 60 60 69 77 81 84 86 89
## [69,] 60 60 60 60 73 83 89 95 101 106
## [70,] 60 60 60 70 77 88 95 103 111 118
## [71,] 60 60 60 73 85 92 100 109 121 120
## [72,] 60 60 60 72 83 91 99 107 114 121
## [73,] 60 60 60 70 81 89 96 104 111 117
## [74,] 60 60 60 69 80 87 95 102 109 115
## [75,] 60 60 60 66 78 85 92 99 107 114
## [76,] 59 60 60 67 76 83 90 97 105 112
## [77,] 59 60 60 65 75 82 90 98 106 114
## [78,] 58 59 60 62 72 80 89 97 106 117
## [79,] 57 58 59 60 68 78 88 98 108 120
## [80,] 56 57 58 60 60 74 86 96 108 121
## [81,] 56 57 58 60 60 70 81 91 101 114
## [82,] 55 56 57 59 60 67 75 84 93 108
## [83,] 55 56 57 59 60 63 69 77 87 101
## [,828] [,829] [,830] [,831] [,832] [,833] [,834] [,835] [,836] [,837]
## [1,] 56 58 60 61 62 63 66 68 70 72
## [2,] 58 60 62 63 63 65 68 72 75 77
## [3,] 60 62 64 65 64 66 70 74 77 79
## [4,] 61 62 64 65 64 65 68 72 75 77
## [5,] 61 62 64 64 63 63 65 68 71 73
## [6,] 61 61 63 62 62 62 63 64 66 67
## [7,] 61 61 61 61 61 61 61 61 62 63
## [8,] 61 60 60 60 61 61 60 60 60 61
## [9,] 60 60 60 60 60 60 60 60 60 60
## [10,] 60 60 60 60 60 60 60 60 60 60
## [11,] 60 60 60 60 60 60 60 60 60 60
## [12,] 60 60 60 60 60 60 60 60 60 60
## [13,] 60 60 60 60 60 60 60 60 60 60
## [14,] 60 60 60 60 60 60 60 60 60 60
## [15,] 60 60 60 60 60 60 60 60 60 60
## [16,] 60 60 60 60 60 60 60 60 60 60
## [17,] 60 60 60 60 60 60 60 60 60 61
## [18,] 60 60 60 60 60 60 60 60 60 61
## [19,] 60 60 60 60 60 60 60 60 61 61
## [20,] 60 60 60 60 60 60 60 60 61 62
## [21,] 60 60 60 60 60 60 60 60 61 62
## [22,] 60 60 60 60 60 60 60 60 61 63
## [23,] 60 60 60 60 60 60 60 60 61 64
## [24,] 60 60 60 60 60 60 60 60 61 64
## [25,] 60 60 60 60 60 60 60 60 62 64
## [26,] 60 60 60 60 60 60 60 60 62 64
## [27,] 60 60 60 60 60 60 60 60 61 63
## [28,] 60 60 60 60 60 60 60 60 60 60
## [29,] 60 60 60 60 60 60 60 60 60 60
## [30,] 60 60 60 60 60 60 60 60 60 60
## [31,] 60 60 60 60 60 60 60 60 60 60
## [32,] 60 60 60 60 60 60 60 60 60 60
## [33,] 60 60 60 60 60 60 60 60 60 60
## [34,] 60 60 60 60 60 60 60 60 60 60
## [35,] 60 60 60 60 60 60 60 60 60 60
## [36,] 60 60 60 60 60 60 60 60 60 60
## [37,] 60 60 60 60 60 60 60 60 60 60
## [38,] 60 60 60 60 60 60 60 60 60 60
## [39,] 60 60 60 60 60 60 60 60 60 60
## [40,] 60 60 60 60 60 60 60 60 60 60
## [41,] 60 60 60 60 60 60 60 60 60 60
## [42,] 60 60 60 60 60 60 60 60 60 60
## [43,] 60 60 60 60 60 60 60 60 60 60
## [44,] 60 60 60 60 60 60 60 60 60 60
## [45,] 60 60 61 60 60 60 60 60 60 60
## [46,] 60 66 64 62 60 60 60 60 60 61
## [47,] 77 78 72 65 60 60 60 60 60 64
## [48,] 94 90 82 73 67 60 60 60 60 69
## [49,] 110 107 95 85 78 71 60 60 60 77
## [50,] 131 127 111 99 94 88 82 73 78 88
## [51,] 161 147 121 112 110 107 99 90 93 98
## [52,] 182 172 138 121 121 121 110 101 101 104
## [53,] 182 182 163 156 147 135 126 116 115 112
## [54,] 182 182 182 182 169 154 142 134 123 119
## [55,] 182 182 182 182 182 169 157 147 133 121
## [56,] 167 176 182 182 182 182 172 162 151 152
## [57,] 151 163 176 182 182 182 182 177 173 176
## [58,] 133 151 167 175 182 182 182 182 182 182
## [59,] 121 139 158 169 181 182 182 182 182 182
## [60,] 119 128 147 160 171 182 182 182 182 182
## [61,] 109 121 135 146 159 168 175 182 182 182
## [62,] 92 110 121 131 148 160 170 181 182 182
## [63,] 83 105 120 121 142 157 170 182 182 182
## [64,] 73 109 121 131 140 153 168 182 182 182
## [65,] 60 89 121 127 139 152 166 182 182 157
## [66,] 60 60 75 112 127 141 158 178 170 147
## [67,] 71 60 89 96 111 121 142 153 150 133
## [68,] 93 91 95 104 113 119 126 133 130 121
## [69,] 117 110 111 114 117 119 120 122 121 123
## [70,] 120 121 120 119 120 121 121 121 121 121
## [71,] 121 122 121 121 121 121 121 121 121 121
## [72,] 121 122 124 124 121 121 121 121 121 121
## [73,] 121 124 126 128 128 130 127 121 121 121
## [74,] 121 125 128 131 135 138 140 140 133 121
## [75,] 121 126 131 136 142 148 156 164 169 149
## [76,] 120 129 135 142 149 157 170 182 179 182
## [77,] 121 128 135 143 151 160 174 181 182 182
## [78,] 120 121 131 140 149 157 170 182 182 182
## [79,] 121 121 124 135 145 155 169 181 182 182
## [80,] 121 121 121 133 143 153 168 182 182 182
## [81,] 121 121 130 136 144 152 166 179 182 182
## [82,] 121 121 129 137 144 151 162 172 177 182
## [83,] 114 121 128 135 142 149 159 168 174 178
## [,838] [,839] [,840] [,841] [,842] [,843] [,844] [,845] [,846] [,847]
## [1,] 72 72 70 67 64 61 57 54 52 50
## [2,] 77 76 74 71 68 65 62 59 57 55
## [3,] 79 78 76 73 70 67 64 62 61 59
## [4,] 78 76 74 71 69 66 64 62 61 60
## [5,] 73 72 70 67 65 63 62 61 60 60
## [6,] 68 67 65 63 62 61 60 60 60 60
## [7,] 63 63 62 61 60 60 60 60 60 60
## [8,] 61 61 60 60 60 60 60 60 60 60
## [9,] 60 60 60 60 60 60 60 60 60 60
## [10,] 60 60 60 60 60 60 60 60 60 60
## [11,] 60 60 60 60 60 60 60 60 60 60
## [12,] 60 60 60 60 60 60 60 60 60 60
## [13,] 60 60 60 60 60 60 60 60 60 60
## [14,] 60 61 60 60 60 60 60 60 60 60
## [15,] 61 61 62 61 61 61 61 61 60 60
## [16,] 61 62 62 62 62 62 62 61 60 60
## [17,] 62 63 63 63 63 63 64 63 60 60
## [18,] 62 64 65 65 65 66 67 67 69 70
## [19,] 64 66 66 67 67 68 70 72 74 79
## [20,] 64 67 68 69 71 73 75 78 83 88
## [21,] 65 68 71 73 76 78 81 85 91 96
## [22,] 66 70 74 77 81 84 87 92 97 101
## [23,] 68 71 75 78 82 85 88 93 98 101
## [24,] 69 73 75 78 81 84 87 91 95 98
## [25,] 69 72 75 77 80 82 84 88 91 93
## [26,] 67 70 72 74 76 78 80 83 84 86
## [27,] 65 67 68 70 71 72 74 73 73 74
## [28,] 61 62 63 63 64 64 65 60 60 60
## [29,] 60 60 61 61 61 60 61 61 60 60
## [30,] 60 60 60 60 60 60 60 60 60 60
## [31,] 60 60 60 60 60 60 60 60 60 60
## [32,] 60 60 60 60 60 60 60 60 60 60
## [33,] 60 60 60 60 60 60 60 60 60 60
## [34,] 60 60 60 60 60 60 60 60 60 60
## [35,] 60 60 60 60 60 60 60 60 60 60
## [36,] 60 60 60 60 60 60 60 60 60 60
## [37,] 60 60 60 60 60 60 60 60 60 60
## [38,] 60 60 60 60 60 60 60 60 60 60
## [39,] 60 60 60 60 60 60 60 60 60 60
## [40,] 60 60 60 60 60 60 60 60 60 60
## [41,] 60 60 60 60 60 60 60 60 60 60
## [42,] 60 60 60 60 60 60 60 60 60 60
## [43,] 60 60 60 60 60 60 60 60 60 60
## [44,] 60 60 60 60 60 60 60 60 60 60
## [45,] 60 60 60 60 60 60 60 60 60 60
## [46,] 60 60 60 60 60 61 60 60 60 60
## [47,] 63 60 60 63 60 69 65 60 60 60
## [48,] 70 68 68 70 75 80 77 72 70 70
## [49,] 79 78 82 83 86 90 90 88 91 89
## [50,] 86 85 89 90 93 98 99 99 102 102
## [51,] 96 96 99 101 104 109 113 117 117 118
## [52,] 106 108 110 112 115 120 121 138 137 142
## [53,] 113 115 118 119 124 137 153 170 160 163
## [54,] 119 121 134 136 147 167 182 176 182 182
## [55,] 131 146 156 158 166 179 181 186 190 191
## [56,] 153 168 182 182 176 178 182 192 200 206
## [57,] 174 182 180 181 182 181 188 199 211 224
## [58,] 182 181 182 182 182 182 196 208 220 243
## [59,] 182 182 182 182 182 182 191 202 211 223
## [60,] 182 182 182 182 182 182 182 192 195 207
## [61,] 182 182 182 182 182 173 178 182 182 195
## [62,] 182 177 173 166 159 157 163 171 179 182
## [63,] 171 162 152 146 139 141 148 163 176 180
## [64,] 158 142 130 127 124 126 135 159 178 180
## [65,] 142 121 125 122 121 122 121 157 182 181
## [66,] 121 123 122 122 131 142 170 167 182 185
## [67,] 121 121 121 134 162 182 175 182 184 190
## [68,] 124 121 125 150 182 180 182 183 188 196
## [69,] 121 121 135 153 182 182 182 186 192 200
## [70,] 121 121 130 145 164 177 182 185 191 200
## [71,] 121 121 121 130 153 163 173 182 182 188
## [72,] 121 121 121 126 145 155 164 171 178 182
## [73,] 121 121 121 121 133 142 152 160 168 178
## [74,] 121 121 121 121 121 130 138 148 157 170
## [75,] 134 121 121 121 121 121 126 137 146 158
## [76,] 182 150 121 121 121 121 121 127 135 146
## [77,] 182 182 167 129 121 121 121 121 125 134
## [78,] 182 182 182 167 121 121 121 121 121 121
## [79,] 182 182 183 183 171 162 139 131 121 121
## [80,] 182 182 183 184 185 184 182 182 157 143
## [81,] 182 182 184 186 188 187 187 185 182 171
## [82,] 182 182 185 189 192 192 194 194 195 189
## [83,] 182 182 186 191 195 198 201 203 207 205
## [,848] [,849] [,850] [,851] [,852] [,853] [,854] [,855] [,856] [,857]
## [1,] 48 47 46 44 41 38 34 31 29 29
## [2,] 54 53 52 50 47 43 40 37 35 35
## [3,] 58 58 57 54 51 47 44 42 39 39
## [4,] 60 60 59 57 54 49 46 44 41 41
## [5,] 60 60 60 59 56 51 48 45 43 43
## [6,] 60 60 60 59 56 52 49 46 45 45
## [7,] 60 60 60 59 56 52 50 48 47 47
## [8,] 60 60 60 59 56 53 52 50 49 49
## [9,] 60 60 60 59 57 55 54 52 51 52
## [10,] 60 60 60 60 58 57 55 54 53 54
## [11,] 60 60 60 60 60 59 57 56 55 56
## [12,] 60 60 61 60 60 60 58 58 57 57
## [13,] 60 60 64 64 61 60 59 59 59 59
## [14,] 60 60 68 69 66 60 60 60 60 60
## [15,] 60 67 74 76 74 68 63 60 60 60
## [16,] 60 77 82 84 83 78 72 66 60 60
## [17,] 70 81 86 89 89 84 78 71 67 62
## [18,] 77 88 93 97 99 93 87 79 73 67
## [19,] 85 94 100 105 108 103 96 86 78 69
## [20,] 93 100 107 116 117 112 105 93 81 70
## [21,] 101 107 115 121 121 121 114 99 85 70
## [22,] 106 111 118 121 121 121 121 100 82 67
## [23,] 105 109 113 119 121 121 121 101 87 78
## [24,] 101 105 109 116 121 121 110 102 94 88
## [25,] 96 99 103 111 117 121 113 107 103 99
## [26,] 88 92 96 106 115 121 119 116 113 112
## [27,] 75 82 87 100 112 121 121 121 120 120
## [28,] 60 72 75 94 108 114 121 120 121 121
## [29,] 60 60 66 87 101 107 111 115 119 121
## [30,] 60 60 71 84 95 99 103 105 109 112
## [31,] 60 60 70 81 88 91 94 96 99 100
## [32,] 60 60 68 75 80 83 85 86 88 88
## [33,] 60 60 65 70 72 74 75 76 76 76
## [34,] 60 60 60 63 64 65 66 66 64 64
## [35,] 60 60 60 60 61 61 62 61 60 61
## [36,] 60 60 60 60 60 60 60 60 60 60
## [37,] 60 60 60 60 60 60 60 60 60 60
## [38,] 60 60 60 60 60 60 60 60 60 60
## [39,] 60 60 60 60 60 60 60 60 60 60
## [40,] 60 60 60 60 60 60 60 60 60 60
## [41,] 60 60 60 60 60 60 60 60 60 60
## [42,] 60 60 60 60 60 60 60 60 60 60
## [43,] 60 60 60 60 60 60 60 60 60 60
## [44,] 60 60 60 60 60 60 60 60 60 60
## [45,] 60 60 60 60 60 60 60 60 60 60
## [46,] 60 60 60 60 60 60 60 60 60 60
## [47,] 60 60 60 60 60 60 60 60 60 60
## [48,] 65 64 71 64 60 60 60 60 60 60
## [49,] 85 84 83 75 70 65 60 60 60 60
## [50,] 103 96 91 86 81 74 66 60 60 64
## [51,] 122 112 104 99 96 86 76 66 67 74
## [52,] 135 125 121 117 121 103 91 82 86 88
## [53,] 155 146 136 131 127 118 106 99 100 102
## [54,] 172 166 159 158 157 138 121 115 113 116
## [55,] 190 183 177 178 181 172 146 121 120 122
## [56,] 212 199 182 187 184 181 182 121 121 128
## [57,] 235 220 208 196 188 182 161 143 136 141
## [58,] 239 243 227 213 199 182 172 161 163 162
## [59,] 237 243 243 227 213 198 182 176 173 172
## [60,] 225 243 243 243 236 220 210 195 189 185
## [61,] 215 234 243 243 243 243 231 217 209 200
## [62,] 198 223 243 243 243 243 243 237 227 217
## [63,] 182 202 221 243 243 243 243 243 243 233
## [64,] 182 182 192 224 239 243 243 243 243 243
## [65,] 182 182 210 218 231 238 243 243 243 243
## [66,] 189 197 209 220 229 236 240 243 243 243
## [67,] 198 208 216 224 231 238 242 243 243 243
## [68,] 207 220 229 238 240 242 243 243 243 243
## [69,] 215 234 243 240 243 243 243 243 243 243
## [70,] 217 243 241 243 243 243 243 243 243 243
## [71,] 208 222 231 238 243 243 243 243 243 243
## [72,] 194 202 201 214 224 235 243 243 243 243
## [73,] 183 185 183 190 202 214 229 232 237 243
## [74,] 182 182 182 180 182 195 207 209 213 199
## [75,] 170 174 167 169 173 179 190 190 187 183
## [76,] 157 157 155 156 161 167 178 184 182 177
## [77,] 143 145 143 143 149 155 164 171 158 163
## [78,] 130 133 132 130 137 142 149 147 141 147
## [79,] 121 123 123 122 125 129 132 128 126 138
## [80,] 121 121 121 121 122 121 121 122 121 125
## [81,] 139 121 121 121 121 121 121 121 121 121
## [82,] 172 151 139 128 121 121 121 121 121 121
## [83,] 194 182 182 160 139 121 121 121 121 121
## [,858] [,859] [,860] [,861] [,862] [,863] [,864] [,865] [,866] [,867]
## [1,] 31 34 37 41 44 48 51 54 56 58
## [2,] 36 39 43 46 50 52 55 57 58 60
## [3,] 41 45 49 52 55 57 58 60 61 61
## [4,] 44 48 53 56 58 59 60 60 61 63
## [5,] 46 51 55 57 59 60 60 61 63 67
## [6,] 47 51 55 57 59 60 60 62 66 71
## [7,] 49 52 55 56 58 59 60 64 69 76
## [8,] 50 52 55 56 58 59 60 65 73 82
## [9,] 53 54 56 57 58 59 60 62 75 90
## [10,] 55 56 57 57 58 59 60 60 73 96
## [11,] 56 57 57 58 58 59 59 60 63 78
## [12,] 57 57 58 58 58 59 59 59 60 60
## [13,] 58 58 59 59 59 59 59 60 60 60
## [14,] 60 60 60 60 60 60 60 60 60 60
## [15,] 60 60 60 60 60 60 60 60 60 60
## [16,] 60 60 60 60 60 60 60 60 60 60
## [17,] 60 60 60 60 60 60 60 60 60 60
## [18,] 62 60 60 60 60 60 60 60 60 60
## [19,] 63 61 60 60 60 60 60 60 60 60
## [20,] 63 61 60 60 60 60 60 60 60 60
## [21,] 63 60 60 60 60 60 60 60 60 60
## [22,] 60 61 60 60 60 60 60 60 60 60
## [23,] 72 71 72 73 75 77 80 81 81 69
## [24,] 86 87 89 92 97 102 111 111 111 96
## [25,] 100 104 106 108 114 121 134 145 142 121
## [26,] 110 113 114 116 121 134 149 168 182 157
## [27,] 120 121 121 124 137 151 170 180 179 182
## [28,] 121 121 121 130 147 168 181 182 181 182
## [29,] 121 120 121 126 143 167 173 167 176 182
## [30,] 111 115 118 121 121 121 121 121 144 163
## [31,] 102 106 110 113 116 118 121 121 121 147
## [32,] 93 98 103 107 112 116 121 121 135 138
## [33,] 84 90 96 101 107 113 120 121 125 128
## [34,] 74 81 87 94 101 108 117 121 121 121
## [35,] 64 71 78 86 94 105 116 121 121 121
## [36,] 60 60 68 75 86 100 111 114 118 120
## [37,] 60 60 60 68 81 96 107 111 115 119
## [38,] 60 60 60 64 76 90 102 108 113 118
## [39,] 60 60 60 66 74 85 97 105 111 118
## [40,] 60 60 60 62 72 84 95 102 110 118
## [41,] 60 60 60 67 71 81 91 98 105 111
## [42,] 60 60 60 67 72 78 85 92 99 105
## [43,] 60 60 60 65 69 72 78 85 92 99
## [44,] 60 60 60 62 63 64 70 78 86 93
## [45,] 60 60 60 60 60 60 60 72 81 89
## [46,] 60 60 60 60 60 60 63 69 78 88
## [47,] 60 60 60 60 60 60 60 64 71 80
## [48,] 60 60 60 60 60 60 60 60 60 69
## [49,] 60 60 60 60 60 60 60 60 60 60
## [50,] 60 60 60 60 60 60 60 60 60 60
## [51,] 75 70 64 60 60 60 60 60 60 60
## [52,] 90 84 76 67 60 60 60 60 60 60
## [53,] 105 97 88 79 67 60 60 60 60 60
## [54,] 121 111 100 90 76 60 60 60 60 60
## [55,] 122 121 112 102 88 74 67 62 60 60
## [56,] 130 126 121 113 100 87 80 73 66 60
## [57,] 143 138 131 125 113 95 88 80 72 65
## [58,] 156 149 143 136 121 108 99 90 82 74
## [59,] 165 157 150 144 134 121 110 101 93 87
## [60,] 178 169 163 157 151 131 119 111 105 101
## [61,] 191 182 179 177 182 161 138 121 118 117
## [62,] 207 197 190 186 184 182 158 142 131 128
## [63,] 223 213 206 197 188 182 172 159 155 149
## [64,] 238 228 221 209 199 192 182 176 175 166
## [65,] 243 243 234 222 214 209 196 182 187 182
## [66,] 243 243 243 238 235 234 219 214 204 196
## [67,] 243 243 243 243 243 243 243 232 222 215
## [68,] 243 243 243 243 243 243 243 243 233 227
## [69,] 243 243 243 243 243 243 243 243 243 240
## [70,] 243 243 243 243 243 243 243 243 243 243
## [71,] 243 243 243 243 243 243 243 243 243 243
## [72,] 243 243 243 243 243 243 243 243 243 243
## [73,] 243 243 240 242 243 243 243 243 243 243
## [74,] 182 206 235 242 243 243 243 243 242 242
## [75,] 184 182 226 243 243 243 243 243 242 242
## [76,] 179 182 208 243 243 243 243 243 242 242
## [77,] 166 175 186 206 222 235 243 243 241 241
## [78,] 153 167 178 182 201 222 243 243 238 241
## [79,] 145 163 177 181 182 209 243 243 232 240
## [80,] 133 161 177 181 182 182 197 213 201 237
## [81,] 121 161 179 182 182 182 182 208 243 182
## [82,] 149 173 182 182 182 182 182 190 189 187
## [83,] 143 157 176 182 182 182 184 185 182 182
## [,868] [,869] [,870] [,871] [,872] [,873] [,874] [,875] [,876] [,877]
## [1,] 60 61 63 65 68 70 74 77 79 79
## [2,] 61 62 65 68 72 77 83 86 88 88
## [3,] 63 65 69 73 78 85 91 95 96 96
## [4,] 66 70 74 79 85 92 99 102 104 103
## [5,] 71 76 81 87 93 100 106 109 110 110
## [6,] 78 84 89 95 101 108 112 115 116 116
## [7,] 84 92 98 104 109 114 117 119 120 120
## [8,] 92 101 108 112 115 118 120 121 121 121
## [9,] 103 111 116 118 120 121 121 121 121 121
## [10,] 107 113 118 120 121 121 121 121 121 121
## [11,] 95 106 114 119 121 121 121 121 121 121
## [12,] 82 95 107 118 121 121 121 121 121 121
## [13,] 72 86 101 119 121 121 121 121 121 121
## [14,] 60 73 89 104 117 121 115 118 121 119
## [15,] 60 60 75 90 92 83 96 101 108 114
## [16,] 60 60 60 68 66 60 74 81 90 97
## [17,] 60 60 60 60 60 60 60 60 71 76
## [18,] 60 60 60 60 60 60 60 60 60 60
## [19,] 60 60 60 60 60 60 60 60 60 60
## [20,] 60 60 60 60 60 60 60 60 60 60
## [21,] 60 60 60 60 60 60 60 60 60 60
## [22,] 60 60 60 60 60 60 60 60 60 60
## [23,] 60 60 60 60 60 60 60 60 60 60
## [24,] 87 73 65 60 60 60 60 60 60 60
## [25,] 121 104 89 71 65 60 60 60 60 60
## [26,] 135 121 106 102 88 80 69 60 60 60
## [27,] 172 150 139 132 113 101 95 81 71 66
## [28,] 182 182 182 171 139 121 121 106 95 86
## [29,] 182 182 182 182 172 169 147 128 115 108
## [30,] 176 182 182 182 182 182 182 149 131 121
## [31,] 157 161 172 182 182 172 162 154 139 126
## [32,] 142 144 150 154 145 150 150 151 146 149
## [33,] 127 129 129 126 123 127 149 161 164 169
## [34,] 122 121 122 123 121 159 162 182 182 182
## [35,] 121 121 122 121 147 182 182 177 182 182
## [36,] 121 121 121 121 129 136 152 152 152 160
## [37,] 121 121 121 121 121 121 121 121 121 153
## [38,] 121 121 121 121 121 121 121 121 130 156
## [39,] 121 121 121 121 121 121 121 142 172 182
## [40,] 121 121 121 121 121 133 150 172 178 181
## [41,] 116 121 121 121 121 131 148 154 177 182
## [42,] 111 115 119 121 121 121 128 131 155 176
## [43,] 106 113 119 121 121 121 121 121 135 164
## [44,] 101 111 119 121 121 121 121 121 134 158
## [45,] 98 112 121 121 121 121 121 121 136 147
## [46,] 97 114 121 121 121 121 121 121 130 138
## [47,] 89 101 113 119 121 121 121 121 122 124
## [48,] 77 90 102 110 121 121 121 121 121 121
## [49,] 65 78 88 97 105 116 121 121 117 106
## [50,] 60 65 72 81 87 98 109 112 92 88
## [51,] 60 60 60 66 67 79 88 83 69 71
## [52,] 60 60 60 60 60 60 66 67 60 60
## [53,] 60 60 60 60 60 60 60 60 61 60
## [54,] 60 60 60 60 60 60 60 60 60 60
## [55,] 60 60 60 60 60 60 60 60 60 60
## [56,] 60 60 60 60 60 60 60 60 60 60
## [57,] 60 60 60 60 60 60 60 60 60 60
## [58,] 63 60 60 60 60 60 60 60 60 60
## [59,] 79 73 65 60 60 60 60 60 60 60
## [60,] 98 90 80 76 72 67 62 60 60 60
## [61,] 119 105 93 89 82 76 69 60 60 60
## [62,] 124 118 104 101 96 89 81 69 60 60
## [63,] 136 121 114 113 110 103 90 76 68 60
## [64,] 156 147 134 129 124 117 103 88 78 69
## [65,] 177 182 165 153 140 129 116 100 89 80
## [66,] 185 186 182 170 157 139 125 108 97 90
## [67,] 206 203 191 182 172 152 134 118 109 105
## [68,] 220 223 202 185 182 165 151 136 121 121
## [69,] 240 243 220 192 180 177 170 164 162 167
## [70,] 243 243 243 212 197 182 182 182 182 179
## [71,] 243 243 231 222 213 209 206 197 189 185
## [72,] 243 243 243 233 230 229 228 217 207 195
## [73,] 243 243 243 243 243 243 243 237 221 203
## [74,] 242 242 243 243 243 243 243 243 243 217
## [75,] 242 242 243 243 243 243 243 243 243 237
## [76,] 242 242 242 243 243 243 243 243 243 243
## [77,] 242 242 242 243 243 243 243 243 243 243
## [78,] 242 242 243 243 243 243 243 243 243 244
## [79,] 242 242 243 243 242 243 243 244 244 245
## [80,] 243 243 236 237 239 242 243 244 245 247
## [81,] 182 206 219 226 234 240 243 245 247 250
## [82,] 183 182 203 218 230 239 243 247 250 253
## [83,] 182 201 207 220 234 243 247 250 253 256
## [,878] [,879] [,880] [,881] [,882] [,883] [,884] [,885] [,886] [,887]
## [1,] 79 80 80 81 82 82 82 81 80 78
## [2,] 87 87 87 88 89 89 89 89 88 86
## [3,] 94 93 94 95 96 96 96 97 96 94
## [4,] 101 99 99 100 101 101 102 103 103 103
## [5,] 108 105 105 106 106 107 107 109 110 111
## [6,] 114 111 110 111 111 112 113 114 116 117
## [7,] 119 117 115 116 116 117 117 118 119 120
## [8,] 121 120 120 120 120 120 119 119 120 121
## [9,] 121 121 121 121 121 121 121 121 121 121
## [10,] 121 121 121 121 121 121 121 121 121 121
## [11,] 121 121 121 121 121 121 121 121 121 121
## [12,] 121 121 121 121 121 121 121 121 121 121
## [13,] 121 121 121 121 121 121 121 121 121 121
## [14,] 121 121 121 121 121 121 121 121 121 121
## [15,] 119 121 121 121 121 117 121 120 121 121
## [16,] 108 107 111 112 104 105 103 110 117 118
## [17,] 88 91 95 92 89 89 85 95 106 111
## [18,] 71 75 77 77 75 72 67 82 97 105
## [19,] 60 64 65 65 64 60 61 76 87 96
## [20,] 60 60 61 61 60 61 61 70 78 85
## [21,] 60 60 60 60 60 60 60 66 70 73
## [22,] 60 60 60 60 60 60 60 60 63 64
## [23,] 60 60 60 60 60 60 60 60 60 61
## [24,] 60 60 60 60 60 60 60 60 60 60
## [25,] 60 60 60 60 60 60 60 60 60 60
## [26,] 60 60 60 60 60 60 60 60 60 60
## [27,] 60 60 60 63 60 60 60 60 60 60
## [28,] 80 81 82 74 74 67 60 60 60 60
## [29,] 105 111 103 94 92 87 80 69 67 68
## [30,] 121 124 121 111 110 107 101 91 89 90
## [31,] 142 146 145 138 132 132 117 110 109 113
## [32,] 160 170 182 182 165 160 145 121 121 138
## [33,] 177 181 181 182 182 182 182 158 158 158
## [34,] 180 182 182 182 183 183 183 182 182 182
## [35,] 182 181 182 182 184 185 183 182 182 182
## [36,] 175 180 182 185 187 187 183 182 182 182
## [37,] 170 179 182 192 199 194 184 182 182 182
## [38,] 177 187 204 216 228 209 188 183 182 180
## [39,] 185 203 219 243 238 235 202 186 182 168
## [40,] 192 203 218 236 243 243 211 189 177 156
## [41,] 182 194 208 223 243 243 214 198 187 182
## [42,] 181 182 189 204 214 223 210 197 182 152
## [43,] 178 182 182 182 182 197 198 192 182 151
## [44,] 182 182 182 182 181 185 189 188 182 151
## [45,] 154 162 166 165 178 182 183 183 169 147
## [46,] 135 134 132 121 162 182 182 155 142 132
## [47,] 125 124 121 121 141 169 182 119 86 91
## [48,] 121 121 116 121 119 127 121 60 71 62
## [49,] 108 108 99 98 90 91 66 69 63 62
## [50,] 86 77 71 60 62 61 60 65 61 60
## [51,] 65 62 60 62 60 61 61 60 72 88
## [52,] 61 60 60 60 60 60 60 86 101 121
## [53,] 60 60 60 60 60 69 86 99 115 119
## [54,] 60 60 60 60 72 90 97 104 113 121
## [55,] 60 60 60 81 99 105 108 110 114 121
## [56,] 60 60 81 111 120 121 121 119 119 120
## [57,] 60 60 60 108 120 121 121 121 121 121
## [58,] 60 60 60 87 121 121 121 121 121 121
## [59,] 60 60 60 60 90 121 121 121 121 121
## [60,] 60 60 60 60 60 95 121 121 121 121
## [61,] 60 60 60 60 72 87 121 121 121 121
## [62,] 60 60 60 60 60 69 75 100 114 120
## [63,] 60 60 60 60 60 60 60 60 97 121
## [64,] 60 60 60 60 60 60 60 60 91 133
## [65,] 71 60 60 60 60 60 60 77 90 128
## [66,] 82 72 60 60 60 60 60 71 87 113
## [67,] 101 90 78 63 60 60 60 60 67 106
## [68,] 121 109 96 74 60 60 60 60 60 106
## [69,] 147 127 114 86 66 60 60 60 60 110
## [70,] 182 145 113 89 80 71 60 71 108 116
## [71,] 182 158 115 99 93 86 90 89 114 120
## [72,] 185 182 118 110 106 104 108 109 119 121
## [73,] 185 177 145 120 119 119 130 125 121 121
## [74,] 201 182 163 154 152 158 158 145 130 121
## [75,] 221 206 185 178 188 182 182 160 140 121
## [76,] 243 228 210 209 209 196 189 182 163 131
## [77,] 243 243 226 227 227 215 202 192 173 139
## [78,] 244 244 244 244 243 237 219 204 187 159
## [79,] 246 246 247 245 245 243 232 217 196 182
## [80,] 249 251 250 249 248 245 240 226 204 182
## [81,] 252 255 254 255 254 250 243 236 213 194
## [82,] 256 261 262 267 270 263 254 243 225 206
## [83,] 259 270 282 292 304 285 270 255 237 218
## [,888] [,889] [,890] [,891] [,892] [,893] [,894] [,895] [,896] [,897]
## [1,] 76 74 71 68 64 61 59 58 58 57
## [2,] 85 83 81 76 71 68 66 64 62 60
## [3,] 94 93 91 83 78 76 74 72 67 63
## [4,] 104 103 102 96 89 86 84 79 76 70
## [5,] 112 112 111 107 101 98 96 92 86 80
## [6,] 118 118 118 115 112 108 107 105 101 94
## [7,] 121 121 121 121 120 117 116 115 112 107
## [8,] 121 121 122 122 122 122 122 123 121 118
## [9,] 121 122 123 123 123 125 125 126 128 128
## [10,] 121 123 124 124 125 127 128 131 135 139
## [11,] 121 123 124 125 126 129 132 137 143 150
## [12,] 121 123 125 126 127 129 136 145 154 162
## [13,] 121 121 122 123 121 121 131 150 164 174
## [14,] 121 121 121 121 121 121 134 158 177 181
## [15,] 121 121 121 121 121 141 153 182 178 181
## [16,] 119 120 121 121 121 138 153 162 175 181
## [17,] 116 120 121 121 121 133 142 149 157 157
## [18,] 112 121 121 121 121 124 129 133 136 134
## [19,] 103 110 121 121 121 121 121 122 123 124
## [20,] 90 94 104 113 114 119 121 121 121 122
## [21,] 75 74 85 94 100 108 111 113 117 121
## [22,] 64 60 73 83 92 100 104 105 110 113
## [23,] 60 61 60 69 80 89 93 94 99 105
## [24,] 60 60 60 60 68 79 82 83 88 97
## [25,] 60 60 60 60 60 69 71 72 78 86
## [26,] 60 60 60 60 60 60 60 60 67 74
## [27,] 60 60 60 60 60 60 60 60 60 64
## [28,] 60 60 60 60 60 60 60 60 60 60
## [29,] 68 68 65 60 60 60 60 60 60 60
## [30,] 91 91 82 70 60 60 60 60 60 60
## [31,] 114 114 100 88 82 73 60 60 60 60
## [32,] 141 130 116 108 99 90 81 79 72 62
## [33,] 161 149 129 121 111 101 98 97 89 77
## [34,] 182 174 163 141 128 116 115 115 100 89
## [35,] 182 182 182 167 151 146 138 129 116 103
## [36,] 182 182 182 182 175 173 162 150 133 117
## [37,] 182 182 182 182 182 182 182 170 152 130
## [38,] 182 182 174 179 182 182 182 182 154 134
## [39,] 151 155 158 164 167 174 182 164 143 132
## [40,] 121 132 141 146 148 152 146 145 138 125
## [41,] 121 121 125 128 130 128 121 128 124 123
## [42,] 121 121 121 123 124 121 123 121 122 121
## [43,] 121 117 121 121 121 122 120 121 121 121
## [44,] 121 111 121 121 121 121 117 118 119 120
## [45,] 121 83 94 112 121 113 111 115 117 119
## [46,] 121 64 60 81 89 94 100 114 117 118
## [47,] 67 65 62 61 67 73 93 113 117 118
## [48,] 61 62 61 60 61 60 91 114 118 119
## [49,] 61 61 60 79 87 110 132 147 132 126
## [50,] 60 60 109 133 148 159 182 181 164 147
## [51,] 98 105 162 177 184 190 204 209 191 173
## [52,] 121 153 182 182 187 207 228 243 222 197
## [53,] 146 167 172 182 194 212 243 241 243 211
## [54,] 161 182 182 182 186 200 216 238 233 222
## [55,] 141 164 182 182 182 182 197 205 226 230
## [56,] 125 144 154 169 169 172 179 184 191 222
## [57,] 121 121 121 138 137 151 166 181 199 211
## [58,] 121 121 121 121 121 131 153 182 192 205
## [59,] 121 121 121 121 121 121 131 167 182 192
## [60,] 121 121 121 129 135 142 137 156 174 182
## [61,] 121 121 139 152 167 182 177 172 182 189
## [62,] 130 147 158 175 181 180 182 182 180 182
## [63,] 166 172 173 182 182 181 182 182 182 182
## [64,] 161 182 182 181 182 182 182 182 182 182
## [65,] 144 158 173 182 182 182 182 182 182 182
## [66,] 121 137 144 156 165 174 179 182 182 173
## [67,] 119 121 121 130 141 147 154 164 162 159
## [68,] 118 120 121 121 121 121 134 148 158 160
## [69,] 119 121 121 121 121 121 121 130 177 182
## [70,] 121 121 121 121 121 121 121 121 121 182
## [71,] 121 121 121 121 121 121 121 121 121 131
## [72,] 121 121 121 121 121 121 121 121 121 121
## [73,] 121 121 121 121 121 121 121 121 121 121
## [74,] 121 121 121 121 121 121 121 121 121 121
## [75,] 121 121 121 121 121 121 121 121 121 121
## [76,] 121 121 121 121 121 121 121 121 121 121
## [77,] 121 121 121 121 121 121 121 121 121 121
## [78,] 131 121 121 121 121 121 121 121 121 121
## [79,] 150 121 121 121 121 121 121 121 121 121
## [80,] 165 148 130 121 121 121 121 121 121 121
## [81,] 182 167 151 134 121 121 121 121 121 121
## [82,] 195 186 173 149 129 121 121 121 121 121
## [83,] 206 195 182 170 145 121 121 121 121 121
## [,898] [,899] [,900] [,901] [,902] [,903] [,904] [,905] [,906] [,907]
## [1,] 57 56 56 56 56 57 58 60 62 66
## [2,] 58 56 54 54 54 55 57 60 63 66
## [3,] 60 57 54 53 54 55 57 60 63 67
## [4,] 66 61 59 57 57 57 58 60 62 65
## [5,] 74 70 67 65 63 62 62 62 62 63
## [6,] 87 81 78 75 73 70 69 66 65 65
## [7,] 100 94 90 87 85 82 79 75 74 73
## [8,] 113 108 104 101 99 95 92 87 85 84
## [9,] 127 122 118 116 114 109 105 100 98 96
## [10,] 141 142 138 136 134 128 120 119 117 113
## [11,] 156 161 160 158 154 146 134 142 136 129
## [12,] 173 181 182 182 176 169 163 166 155 143
## [13,] 181 182 181 182 182 182 180 181 182 166
## [14,] 181 181 182 182 182 182 182 182 182 182
## [15,] 181 182 182 164 166 171 178 182 182 182
## [16,] 182 164 150 133 143 155 173 182 182 182
## [17,] 150 121 121 128 121 143 168 182 182 182
## [18,] 125 124 123 122 121 135 162 181 178 182
## [19,] 123 122 121 122 121 121 139 142 160 170
## [20,] 122 121 121 121 121 121 121 121 138 154
## [21,] 120 120 121 121 121 121 121 121 121 129
## [22,] 115 117 120 121 121 121 121 121 121 121
## [23,] 111 115 119 121 121 121 121 121 136 170
## [24,] 106 113 121 121 121 121 121 121 147 163
## [25,] 97 104 111 118 121 121 121 121 140 151
## [26,] 88 94 101 108 114 121 121 121 130 136
## [27,] 79 85 91 98 103 107 116 121 121 123
## [28,] 71 74 81 87 92 99 109 115 121 120
## [29,] 63 64 71 77 81 89 99 106 109 116
## [30,] 60 60 60 67 69 78 89 97 102 109
## [31,] 60 60 60 60 60 72 83 91 97 103
## [32,] 60 60 60 60 60 64 73 81 88 94
## [33,] 66 60 60 60 60 60 60 69 73 76
## [34,] 83 75 66 60 60 60 60 60 60 60
## [35,] 99 94 84 72 60 60 60 60 60 60
## [36,] 116 114 103 90 79 67 62 60 60 60
## [37,] 124 122 121 109 91 76 68 66 63 60
## [38,] 128 124 121 118 99 83 75 73 70 69
## [39,] 128 125 123 121 106 88 81 80 77 76
## [40,] 124 124 123 121 108 92 85 84 82 81
## [41,] 121 121 122 122 111 97 92 91 89 89
## [42,] 122 121 121 121 105 101 99 98 96 96
## [43,] 121 121 121 121 110 107 105 105 104 104
## [44,] 120 121 121 121 116 113 112 112 111 112
## [45,] 120 120 120 121 120 119 118 119 118 119
## [46,] 119 120 120 121 121 121 121 123 121 124
## [47,] 119 120 120 121 121 121 127 131 136 135
## [48,] 120 120 121 121 122 121 138 142 147 148
## [49,] 121 121 121 121 134 142 149 154 158 162
## [50,] 131 121 121 143 148 155 160 166 170 176
## [51,] 153 140 154 157 160 164 168 173 177 182
## [52,] 182 176 182 175 176 178 179 187 187 184
## [53,] 197 182 187 187 195 195 200 203 198 194
## [54,] 219 220 214 216 214 215 218 224 218 208
## [55,] 243 243 243 240 234 234 236 243 243 230
## [56,] 241 243 248 256 253 243 243 246 244 243
## [57,] 227 243 255 288 304 304 284 255 247 244
## [58,] 219 232 241 255 293 304 288 266 248 244
## [59,] 210 228 239 252 270 272 272 253 243 243
## [60,] 208 238 242 246 261 256 252 246 245 238
## [61,] 198 217 243 240 243 248 248 246 243 229
## [62,] 182 201 215 238 243 243 245 245 243 221
## [63,] 181 182 191 214 238 243 243 243 243 222
## [64,] 180 178 179 192 222 243 243 243 243 214
## [65,] 177 173 172 181 201 215 226 227 215 202
## [66,] 168 160 159 182 182 186 182 191 182 187
## [67,] 148 129 129 153 169 169 167 161 143 146
## [68,] 153 121 122 121 138 137 134 121 127 123
## [69,] 182 167 128 122 121 125 124 122 121 121
## [70,] 182 182 153 121 121 121 121 121 121 121
## [71,] 165 182 165 121 121 121 121 121 121 121
## [72,] 121 182 151 121 121 121 121 121 121 121
## [73,] 121 121 140 121 121 121 121 121 121 121
## [74,] 121 121 123 123 122 121 121 121 121 131
## [75,] 121 121 121 121 123 122 121 121 123 139
## [76,] 121 121 121 121 121 121 121 121 124 137
## [77,] 121 121 121 121 121 121 121 121 121 131
## [78,] 121 121 121 121 121 121 121 121 121 121
## [79,] 121 121 121 121 121 121 121 121 121 121
## [80,] 121 121 121 121 121 121 121 121 121 121
## [81,] 121 121 121 121 121 121 121 121 121 121
## [82,] 121 121 121 121 121 121 121 121 121 121
## [83,] 121 121 121 121 121 121 121 121 121 121
## [,908] [,909] [,910] [,911] [,912] [,913] [,914] [,915] [,916] [,917]
## [1,] 70 75 81 87 94 100 105 110 114 118
## [2,] 71 76 81 87 94 100 106 111 115 119
## [3,] 72 76 81 87 95 102 109 114 118 121
## [4,] 68 72 76 84 94 103 110 115 118 121
## [5,] 65 67 72 82 93 104 112 117 120 121
## [6,] 66 67 72 84 96 107 115 119 121 121
## [7,] 73 73 79 91 103 112 117 120 121 121
## [8,] 83 82 88 98 108 115 119 121 121 121
## [9,] 95 92 95 103 112 118 121 121 121 121
## [10,] 110 105 105 110 116 120 121 121 121 121
## [11,] 123 115 115 118 120 121 121 121 121 121
## [12,] 133 121 121 122 123 121 121 121 121 121
## [13,] 151 136 121 133 129 125 121 121 121 121
## [14,] 175 159 154 145 138 133 126 121 121 121
## [15,] 182 182 171 158 149 143 133 121 121 121
## [16,] 182 182 182 174 172 170 151 130 121 133
## [17,] 182 182 182 182 181 182 182 156 160 159
## [18,] 182 182 182 182 182 182 182 170 170 178
## [19,] 182 182 182 182 182 182 182 182 180 180
## [20,] 171 182 181 182 182 182 182 182 182 182
## [21,] 157 170 179 182 182 182 182 182 182 182
## [22,] 150 173 182 182 182 182 182 182 182 182
## [23,] 172 178 181 181 182 182 182 182 182 182
## [24,] 182 182 181 176 179 182 182 182 182 182
## [25,] 161 174 171 165 173 182 182 182 182 182
## [26,] 142 149 129 147 160 171 182 182 182 182
## [27,] 125 125 122 126 144 154 162 170 173 170
## [28,] 121 121 121 121 130 136 139 140 145 138
## [29,] 117 120 121 121 121 124 121 121 129 126
## [30,] 114 119 121 121 121 121 121 121 121 122
## [31,] 110 118 121 121 121 121 121 121 120 120
## [32,] 103 115 119 119 121 121 121 121 120 118
## [33,] 86 97 105 113 121 121 121 121 119 116
## [34,] 67 79 87 98 106 115 121 117 113 114
## [35,] 60 65 73 81 87 94 92 106 109 112
## [36,] 60 60 60 66 67 69 68 97 107 111
## [37,] 60 60 60 60 60 60 68 95 105 110
## [38,] 66 64 63 62 60 60 76 96 104 109
## [39,] 74 72 72 70 69 72 92 98 102 108
## [40,] 79 78 78 77 77 80 92 96 104 110
## [41,] 87 87 88 87 88 92 95 101 110 118
## [42,] 95 96 97 98 100 103 106 113 121 122
## [43,] 103 104 106 107 108 110 113 119 128 133
## [44,] 111 111 112 113 114 116 118 120 135 146
## [45,] 117 117 117 118 120 120 121 124 138 151
## [46,] 121 121 121 121 121 121 122 127 142 150
## [47,] 134 128 130 128 126 125 123 126 138 146
## [48,] 147 143 138 134 130 127 124 124 132 139
## [49,] 162 153 146 139 134 128 124 122 127 133
## [50,] 177 162 152 144 136 128 121 121 121 124
## [51,] 181 168 157 147 138 129 121 121 121 121
## [52,] 183 174 163 152 142 132 121 121 121 121
## [53,] 185 177 168 158 147 137 128 121 121 121
## [54,] 193 182 174 164 154 143 128 121 121 121
## [55,] 210 194 182 173 162 150 129 121 121 121
## [56,] 227 212 200 188 177 164 141 121 121 121
## [57,] 243 231 219 205 192 182 152 121 121 121
## [58,] 243 243 237 221 204 184 162 121 121 121
## [59,] 243 243 243 243 224 198 166 131 121 122
## [60,] 235 233 238 243 243 204 167 121 126 122
## [61,] 213 203 212 211 211 200 166 121 121 122
## [62,] 196 182 191 193 182 182 151 121 121 121
## [63,] 182 181 180 184 173 154 130 123 122 122
## [64,] 182 171 166 155 150 135 123 122 121 122
## [65,] 182 158 143 130 127 122 123 122 122 121
## [66,] 150 142 121 125 122 121 122 122 121 121
## [67,] 124 122 123 122 121 121 121 121 121 128
## [68,] 121 122 121 121 121 121 121 121 121 121
## [69,] 121 121 121 121 121 121 121 121 121 125
## [70,] 121 121 121 121 121 121 121 121 121 142
## [71,] 121 121 121 121 121 121 139 145 162 182
## [72,] 121 121 121 121 152 164 170 175 191 199
## [73,] 121 121 162 182 167 182 188 199 217 226
## [74,] 145 172 180 180 181 181 195 207 228 243
## [75,] 157 168 182 181 182 182 182 185 182 213
## [76,] 151 166 182 182 182 181 182 182 183 182
## [77,] 145 159 169 182 169 172 178 181 182 191
## [78,] 136 147 155 154 154 158 168 176 182 182
## [79,] 128 134 138 138 140 142 156 169 182 182
## [80,] 121 123 124 124 122 121 132 151 176 182
## [81,] 121 121 121 121 121 121 121 121 169 182
## [82,] 121 121 121 121 121 121 121 162 182 179
## [83,] 121 121 121 121 121 121 146 170 179 172
## [,918] [,919] [,920] [,921] [,922] [,923] [,924] [,925] [,926] [,927]
## [1,] 123 129 137 145 152 159 163 168 173 177
## [2,] 124 131 139 148 158 167 172 177 180 184
## [3,] 126 135 145 156 167 173 182 188 190 190
## [4,] 127 137 149 161 170 176 181 184 186 187
## [5,] 129 143 156 167 172 175 177 180 182 183
## [6,] 124 134 148 160 165 167 169 172 176 179
## [7,] 121 126 135 146 154 156 159 163 168 174
## [8,] 121 122 127 134 140 142 146 151 159 167
## [9,] 121 121 121 123 126 128 131 138 148 159
## [10,] 121 121 121 121 121 122 123 129 139 149
## [11,] 121 121 121 121 121 121 121 125 133 141
## [12,] 121 121 121 121 121 121 121 124 129 133
## [13,] 121 121 121 121 121 121 121 121 121 121
## [14,] 121 121 121 121 121 121 121 121 121 121
## [15,] 121 121 121 121 121 121 121 121 121 121
## [16,] 150 139 132 127 121 121 121 121 121 121
## [17,] 182 166 160 157 152 135 125 121 121 121
## [18,] 182 182 177 182 168 151 131 122 121 121
## [19,] 182 182 182 181 182 160 132 122 121 121
## [20,] 182 182 182 182 182 160 132 121 121 121
## [21,] 182 182 182 182 182 155 125 122 122 121
## [22,] 182 182 182 182 182 154 128 121 121 121
## [23,] 182 182 182 182 182 153 125 122 122 122
## [24,] 182 182 182 178 159 143 126 123 122 122
## [25,] 182 182 182 172 155 125 122 122 122 122
## [26,] 182 182 182 182 164 134 122 121 122 122
## [27,] 155 164 182 182 182 149 121 121 122 122
## [28,] 121 138 161 169 170 153 124 122 122 122
## [29,] 126 121 137 136 133 121 125 122 122 122
## [30,] 121 122 121 124 121 122 121 122 122 122
## [31,] 121 121 121 121 121 121 121 121 121 121
## [32,] 119 119 120 121 121 121 121 121 121 121
## [33,] 117 118 119 120 120 120 121 121 121 121
## [34,] 115 117 118 119 119 120 120 121 121 121
## [35,] 114 116 118 118 119 119 120 121 121 121
## [36,] 113 115 117 118 118 119 120 120 121 121
## [37,] 112 114 116 117 118 119 120 120 121 121
## [38,] 111 114 116 117 118 119 120 120 121 121
## [39,] 111 113 115 117 118 120 120 121 121 121
## [40,] 112 114 116 118 120 121 121 121 121 121
## [41,] 117 119 120 120 121 121 121 124 121 121
## [42,] 121 131 136 138 127 121 121 136 134 121
## [43,] 141 150 158 163 167 142 149 160 169 163
## [44,] 157 170 182 182 181 182 176 182 180 182
## [45,] 164 177 181 182 182 182 182 186 192 196
## [46,] 161 168 175 182 182 182 186 195 203 211
## [47,] 154 161 168 174 181 182 191 202 214 223
## [48,] 146 153 160 166 174 182 191 205 222 238
## [49,] 141 148 154 164 173 178 182 198 220 243
## [50,] 132 139 147 156 166 172 178 182 205 219
## [51,] 125 132 140 150 160 167 174 182 192 198
## [52,] 121 127 133 143 153 160 167 173 178 181
## [53,] 121 121 126 135 145 152 159 166 169 174
## [54,] 121 121 121 127 136 144 151 158 162 167
## [55,] 121 121 121 121 127 136 143 150 155 161
## [56,] 121 121 121 121 121 128 135 142 149 157
## [57,] 121 121 121 121 121 121 127 135 143 153
## [58,] 121 121 121 121 121 121 121 131 139 150
## [59,] 121 121 121 121 121 121 123 128 134 146
## [60,] 122 121 122 122 121 121 121 127 129 142
## [61,] 122 122 123 122 122 121 121 121 123 136
## [62,] 121 122 124 122 122 121 121 121 121 130
## [63,] 121 121 127 122 122 121 121 121 121 123
## [64,] 121 121 131 121 121 121 121 121 121 121
## [65,] 121 152 183 192 187 167 162 152 131 121
## [66,] 182 170 200 221 209 206 199 190 182 146
## [67,] 151 182 220 240 235 234 223 211 199 180
## [68,] 151 182 223 243 242 245 243 231 214 202
## [69,] 129 162 198 243 243 247 248 243 228 217
## [70,] 121 162 192 243 243 254 260 259 250 237
## [71,] 182 182 179 223 243 263 277 284 270 252
## [72,] 205 205 209 233 253 278 297 302 288 265
## [73,] 231 243 243 259 284 304 296 303 297 277
## [74,] 243 242 259 275 295 302 303 303 302 288
## [75,] 243 243 252 268 281 292 304 304 304 304
## [76,] 209 233 243 255 265 280 296 304 304 304
## [77,] 195 227 242 243 243 259 275 292 304 304
## [78,] 184 184 213 225 233 240 252 276 299 304
## [79,] 182 182 183 182 211 230 243 255 267 284
## [80,] 182 182 182 194 200 219 243 243 243 243
## [81,] 182 182 182 186 189 192 199 225 234 240
## [82,] 182 182 180 181 182 182 182 195 226 239
## [83,] 169 170 176 181 182 182 182 199 217 234
## [,928] [,929] [,930] [,931] [,932] [,933] [,934] [,935] [,936] [,937]
## [1,] 179 179 179 179 180 182 186 189 187 180
## [2,] 186 186 188 187 186 189 193 195 192 185
## [3,] 192 194 194 192 191 194 198 199 196 189
## [4,] 188 190 192 192 192 194 197 197 194 186
## [5,] 184 186 188 189 192 195 196 194 191 187
## [6,] 182 183 185 188 195 201 201 196 191 188
## [7,] 178 181 185 193 201 210 207 200 193 189
## [8,] 174 179 188 201 214 222 215 205 196 190
## [9,] 170 175 188 214 230 236 229 210 196 188
## [10,] 160 168 179 205 225 235 232 208 194 187
## [11,] 150 160 174 191 217 229 220 208 195 187
## [12,] 141 150 160 173 191 205 204 200 182 186
## [13,] 130 138 148 161 174 182 188 188 182 182
## [14,] 121 126 135 149 163 173 182 184 184 182
## [15,] 121 121 121 136 151 161 171 182 182 181
## [16,] 121 121 121 126 142 152 160 169 182 175
## [17,] 121 121 121 121 126 137 141 147 145 158
## [18,] 121 121 121 121 121 121 121 121 121 140
## [19,] 121 121 121 121 121 121 121 121 121 127
## [20,] 121 121 121 121 121 121 121 121 121 124
## [21,] 121 121 121 121 121 121 121 121 121 121
## [22,] 121 121 121 121 121 121 121 121 121 121
## [23,] 121 121 121 121 121 121 121 121 121 121
## [24,] 121 121 121 121 121 121 121 121 121 121
## [25,] 122 121 121 121 121 121 121 121 121 121
## [26,] 121 121 121 121 121 121 121 121 121 121
## [27,] 121 121 121 121 121 121 121 121 121 121
## [28,] 121 121 121 121 121 121 121 121 121 121
## [29,] 121 121 121 121 121 121 121 121 121 121
## [30,] 121 121 121 121 121 121 121 121 121 121
## [31,] 121 121 121 121 121 121 121 121 121 121
## [32,] 121 121 121 121 121 121 121 121 121 121
## [33,] 121 121 121 121 121 121 121 121 121 121
## [34,] 121 121 121 121 121 121 121 121 121 121
## [35,] 121 121 121 121 121 121 121 121 121 121
## [36,] 121 121 121 121 121 121 121 121 121 121
## [37,] 121 121 121 121 121 121 121 121 121 121
## [38,] 121 121 121 121 121 121 121 121 121 121
## [39,] 121 122 122 121 121 121 121 121 121 121
## [40,] 121 125 124 121 121 121 121 121 121 121
## [41,] 121 132 130 126 123 121 121 121 121 121
## [42,] 149 140 137 133 128 121 121 121 121 121
## [43,] 166 165 151 145 140 129 121 135 133 121
## [44,] 182 182 171 164 164 158 161 163 182 163
## [45,] 199 192 186 180 187 188 188 188 188 185
## [46,] 221 216 205 206 204 204 203 204 205 201
## [47,] 238 230 218 218 219 216 214 214 215 214
## [48,] 242 243 237 237 237 232 230 229 231 236
## [49,] 243 243 243 243 243 243 241 239 243 241
## [50,] 236 243 243 243 243 242 242 242 243 243
## [51,] 214 233 243 243 237 240 242 243 243 243
## [52,] 192 212 228 226 230 234 241 243 243 243
## [53,] 179 182 200 210 220 231 242 243 243 243
## [54,] 174 181 186 191 207 224 243 243 243 243
## [55,] 168 176 179 182 182 202 236 243 243 243
## [56,] 166 172 177 181 182 194 227 241 243 243
## [57,] 163 170 176 182 184 202 233 243 250 265
## [58,] 161 168 175 182 186 202 225 243 255 275
## [59,] 158 166 174 182 189 199 218 235 243 266
## [60,] 154 163 172 182 188 196 212 231 243 253
## [61,] 148 156 165 172 179 186 205 228 241 249
## [62,] 140 149 157 165 172 178 194 224 243 250
## [63,] 132 140 149 159 167 179 194 213 227 239
## [64,] 121 132 143 153 163 175 182 202 217 229
## [65,] 121 124 140 151 161 173 182 195 210 224
## [66,] 121 141 144 155 163 177 186 197 211 225
## [67,] 171 162 162 164 168 176 182 200 216 232
## [68,] 190 182 178 175 175 178 182 197 219 243
## [69,] 205 193 182 182 180 180 181 182 213 228
## [70,] 225 212 208 197 191 184 182 182 204 222
## [71,] 243 231 229 218 215 202 182 202 208 222
## [72,] 255 247 243 237 236 227 219 220 227 237
## [73,] 265 254 245 244 243 243 237 238 243 241
## [74,] 274 257 243 243 243 243 243 243 243 243
## [75,] 287 263 243 243 243 243 243 243 243 243
## [76,] 298 272 243 243 243 243 243 243 243 243
## [77,] 304 280 243 243 243 243 243 243 243 243
## [78,] 304 293 267 243 243 241 243 243 243 243
## [79,] 304 277 261 254 243 231 228 237 243 243
## [80,] 243 269 260 251 243 216 203 215 226 238
## [81,] 243 243 247 248 245 192 186 190 206 220
## [82,] 243 243 243 243 244 243 182 185 182 198
## [83,] 243 243 243 243 243 243 196 182 183 182
## [,938] [,939] [,940] [,941] [,942] [,943] [,944] [,945] [,946] [,947]
## [1,] 170 158 147 138 131 130 132 137 140 138
## [2,] 173 159 147 139 134 134 140 146 150 147
## [3,] 172 156 144 141 137 143 151 156 159 154
## [4,] 173 158 150 154 158 158 163 167 164 154
## [5,] 180 174 167 173 179 176 176 175 169 159
## [6,] 185 182 187 193 201 193 188 181 171 160
## [7,] 189 192 202 214 218 211 200 187 173 158
## [8,] 191 200 213 221 226 218 207 192 175 157
## [9,] 191 197 204 214 228 223 205 186 171 155
## [10,] 187 190 194 203 209 200 187 174 161 145
## [11,] 184 184 187 195 212 199 186 175 163 151
## [12,] 183 182 182 197 226 210 187 179 177 165
## [13,] 182 182 182 182 243 243 211 203 192 182
## [14,] 181 182 182 182 243 243 227 224 210 194
## [15,] 180 182 182 206 232 243 242 243 235 214
## [16,] 178 182 182 194 210 225 243 243 234 231
## [17,] 167 174 179 182 190 204 215 232 240 243
## [18,] 156 164 172 182 182 182 185 204 222 243
## [19,] 144 152 159 167 176 179 180 182 193 203
## [20,] 134 140 143 153 160 167 174 179 181 182
## [21,] 125 126 127 137 149 161 171 178 181 182
## [22,] 121 121 121 121 139 158 173 179 182 206
## [23,] 121 121 121 128 140 162 176 182 197 211
## [24,] 121 121 125 138 151 173 181 182 187 202
## [25,] 121 121 128 139 152 174 182 180 182 182
## [26,] 121 121 129 138 149 168 176 178 181 182
## [27,] 121 121 121 130 140 156 165 174 182 180
## [28,] 121 121 121 121 126 145 151 158 164 171
## [29,] 121 121 121 121 127 132 135 143 152 160
## [30,] 121 121 121 121 121 123 122 127 139 148
## [31,] 121 121 121 121 121 121 121 121 129 137
## [32,] 121 121 121 121 121 121 121 124 124 126
## [33,] 121 121 121 121 121 121 121 121 121 121
## [34,] 121 121 121 121 121 121 121 121 121 121
## [35,] 121 121 121 121 121 121 121 121 121 121
## [36,] 121 121 121 121 121 121 121 121 121 121
## [37,] 121 121 121 121 121 121 121 121 121 121
## [38,] 121 121 121 121 121 121 121 121 121 121
## [39,] 121 121 121 121 121 121 121 121 121 121
## [40,] 121 121 121 121 121 121 121 121 121 121
## [41,] 121 121 121 121 121 121 121 121 121 121
## [42,] 121 121 129 121 126 121 121 121 121 121
## [43,] 131 145 156 171 158 131 121 121 121 121
## [44,] 155 165 182 181 183 161 148 121 131 121
## [45,] 178 176 182 186 183 182 182 182 152 145
## [46,] 192 182 188 188 184 183 182 182 182 182
## [47,] 205 201 198 192 185 183 182 182 182 182
## [48,] 224 214 207 194 184 183 182 182 182 182
## [49,] 243 229 221 194 184 182 182 182 182 182
## [50,] 243 243 243 223 189 182 182 182 182 182
## [51,] 243 243 243 243 202 182 182 182 182 182
## [52,] 243 243 243 236 192 186 182 182 182 180
## [53,] 243 243 243 231 204 182 198 195 188 182
## [54,] 247 249 247 236 220 221 219 214 208 196
## [55,] 256 265 267 251 243 243 243 232 227 221
## [56,] 264 277 284 279 274 264 252 243 240 237
## [57,] 282 297 303 304 304 295 280 265 248 244
## [58,] 304 299 304 304 304 304 304 289 256 247
## [59,] 284 291 291 284 274 274 289 278 253 246
## [60,] 274 267 261 243 248 244 243 243 243 246
## [61,] 265 260 252 245 243 244 240 233 230 217
## [62,] 258 253 249 247 246 243 235 223 206 185
## [63,] 247 247 248 249 249 246 244 235 210 186
## [64,] 238 243 248 253 252 249 246 243 215 196
## [65,] 235 243 256 268 263 255 247 243 226 209
## [66,] 236 243 278 304 283 264 248 243 237 230
## [67,] 243 261 290 299 304 270 243 243 243 243
## [68,] 249 263 293 304 304 287 286 282 289 280
## [69,] 243 259 293 304 304 304 304 304 303 304
## [70,] 235 258 286 299 304 304 304 304 304 294
## [71,] 235 255 277 285 289 297 304 304 304 304
## [72,] 242 257 267 273 275 278 285 294 302 304
## [73,] 243 250 256 258 259 258 261 270 285 298
## [74,] 243 243 246 246 246 244 243 250 266 280
## [75,] 243 243 243 243 243 242 242 242 249 264
## [76,] 243 243 243 243 243 242 240 240 243 253
## [77,] 243 243 243 243 243 241 238 232 234 240
## [78,] 243 243 243 243 243 240 235 223 222 229
## [79,] 243 243 243 243 243 237 228 205 207 217
## [80,] 243 243 243 243 243 243 227 194 182 199
## [81,] 238 243 243 243 243 243 243 197 182 182
## [82,] 221 243 243 243 243 243 243 203 182 182
## [83,] 199 224 238 243 243 243 243 213 182 182
## [,948] [,949] [,950] [,951] [,952] [,953] [,954] [,955] [,956] [,957]
## [1,] 133 125 117 109 104 99 97 98 100 102
## [2,] 140 132 124 116 111 106 103 102 102 103
## [3,] 145 137 129 122 115 109 105 104 104 104
## [4,] 143 134 128 122 117 111 108 107 107 107
## [5,] 147 136 128 122 117 113 111 110 111 111
## [6,] 148 137 129 123 119 116 115 114 115 116
## [7,] 145 135 128 123 121 120 119 118 119 124
## [8,] 143 133 126 123 121 121 121 123 125 133
## [9,] 138 128 124 122 121 121 123 131 131 144
## [10,] 135 128 124 122 121 121 131 143 157 162
## [11,] 137 131 124 122 121 121 142 162 170 175
## [12,] 147 135 121 122 121 121 162 182 178 183
## [13,] 164 152 140 125 134 156 182 180 182 186
## [14,] 182 170 158 148 154 170 173 182 182 190
## [15,] 196 182 176 169 171 177 179 180 182 195
## [16,] 209 182 182 185 178 182 181 181 182 196
## [17,] 234 213 206 204 202 196 193 187 182 204
## [18,] 237 240 240 235 243 227 223 210 210 220
## [19,] 219 231 241 243 242 245 244 235 231 235
## [20,] 195 217 235 243 243 253 250 243 243 243
## [21,] 195 215 236 255 272 286 269 252 243 244
## [22,] 223 243 250 274 304 297 304 283 264 245
## [23,] 243 238 250 274 286 304 302 304 271 248
## [24,] 220 234 244 263 276 301 293 279 258 242
## [25,] 207 215 228 243 243 243 270 263 250 236
## [26,] 195 201 208 217 234 248 246 249 247 244
## [27,] 182 186 188 182 203 226 243 245 244 244
## [28,] 177 182 183 183 182 201 223 243 243 243
## [29,] 168 179 182 180 181 182 200 221 243 243
## [30,] 157 170 182 177 177 179 182 192 228 243
## [31,] 146 159 166 173 173 177 182 191 213 243
## [32,] 134 146 152 155 161 168 176 182 209 243
## [33,] 121 132 137 138 148 159 170 179 196 232
## [34,] 121 123 121 121 137 155 169 182 193 206
## [35,] 121 121 121 121 121 145 165 182 183 186
## [36,] 121 121 121 121 121 141 162 182 182 182
## [37,] 121 121 121 121 121 141 162 182 182 182
## [38,] 121 121 121 121 121 141 161 182 182 182
## [39,] 121 121 121 121 126 138 156 182 182 182
## [40,] 121 121 121 121 121 121 140 172 182 182
## [41,] 121 121 121 121 121 121 121 149 174 182
## [42,] 121 121 121 121 121 121 121 129 151 165
## [43,] 121 121 121 121 121 121 121 121 136 147
## [44,] 121 121 121 121 121 121 121 121 121 124
## [45,] 121 121 121 121 121 121 121 121 121 121
## [46,] 150 121 121 121 121 121 121 121 121 121
## [47,] 175 143 121 121 121 121 121 121 121 121
## [48,] 182 173 141 121 121 121 121 121 121 121
## [49,] 182 182 153 121 121 121 121 121 121 121
## [50,] 179 173 155 136 121 121 121 121 121 121
## [51,] 174 161 148 133 121 121 121 121 121 121
## [52,] 169 163 150 130 124 121 129 127 121 121
## [53,] 180 182 167 149 144 145 150 156 133 121
## [54,] 186 181 182 161 158 161 168 182 144 130
## [55,] 205 187 178 177 178 177 180 156 148 140
## [56,] 218 206 197 189 183 182 182 161 152 146
## [57,] 237 223 210 198 183 183 182 166 160 155
## [58,] 244 243 228 213 198 182 182 172 168 164
## [59,] 244 243 243 236 216 194 182 179 177 174
## [60,] 244 244 243 243 235 199 182 182 182 181
## [61,] 244 243 243 243 225 193 184 183 183 182
## [62,] 182 182 243 202 182 184 183 182 183 182
## [63,] 183 199 187 183 185 183 183 183 182 182
## [64,] 182 182 186 182 182 183 182 182 182 182
## [65,] 207 192 182 188 182 182 182 182 182 182
## [66,] 234 219 212 202 194 184 182 182 182 182
## [67,] 245 243 229 218 207 190 182 182 182 182
## [68,] 259 248 244 237 224 210 187 182 182 182
## [69,] 270 250 243 243 243 231 198 182 182 182
## [70,] 253 243 245 243 244 239 206 182 182 182
## [71,] 304 304 274 262 247 243 214 182 182 182
## [72,] 304 304 304 282 254 239 223 195 182 193
## [73,] 304 304 304 294 275 243 243 224 216 211
## [74,] 290 299 304 304 299 279 258 246 230 229
## [75,] 274 284 294 304 304 304 273 254 243 240
## [76,] 263 274 283 292 304 281 273 253 243 242
## [77,] 248 258 265 272 271 263 250 242 242 240
## [78,] 237 243 247 250 247 243 242 234 233 230
## [79,] 227 239 243 244 244 241 235 227 220 214
## [80,] 213 231 243 243 243 239 230 221 210 201
## [81,] 192 229 243 243 243 240 230 217 205 194
## [82,] 182 243 237 242 243 243 236 217 201 189
## [83,] 192 213 243 242 243 243 232 211 188 181
## [,958] [,959] [,960] [,961] [,962] [,963] [,964] [,965] [,966] [,967]
## [1,] 105 108 110 111 113 117 122 129 138 147
## [2,] 105 106 107 108 111 115 122 131 141 150
## [3,] 105 105 105 107 110 115 122 134 146 150
## [4,] 108 108 107 108 111 115 121 129 138 145
## [5,] 112 111 110 111 113 116 120 125 131 137
## [6,] 116 115 114 115 116 118 120 122 126 130
## [7,] 125 123 120 119 119 120 121 121 122 124
## [8,] 134 132 126 124 124 124 123 122 121 121
## [9,] 145 142 133 132 134 131 127 124 122 121
## [10,] 161 156 148 144 147 141 133 127 123 121
## [11,] 175 171 165 160 161 151 140 130 125 123
## [12,] 186 182 182 177 176 166 144 131 132 126
## [13,] 198 200 200 194 188 177 166 153 142 137
## [14,] 214 218 219 210 203 191 181 173 162 152
## [15,] 236 237 237 225 217 205 194 186 177 167
## [16,] 229 243 243 236 229 219 207 195 188 181
## [17,] 238 242 243 242 239 232 221 210 202 196
## [18,] 243 243 242 243 243 240 232 224 217 211
## [19,] 242 243 243 243 243 243 241 236 231 225
## [20,] 243 242 243 243 243 243 243 242 241 236
## [21,] 243 243 243 243 243 241 242 243 243 242
## [22,] 243 241 243 243 243 235 239 243 243 243
## [23,] 239 235 236 243 216 220 232 243 243 243
## [24,] 233 223 215 202 192 189 213 229 243 236
## [25,] 229 215 199 182 188 183 192 211 216 218
## [26,] 238 217 195 185 183 183 182 189 199 201
## [27,] 243 223 182 184 182 183 182 182 182 187
## [28,] 243 243 182 182 183 182 182 182 182 182
## [29,] 243 243 202 182 183 183 182 182 182 182
## [30,] 243 233 196 186 184 182 182 182 182 182
## [31,] 243 243 223 182 183 183 182 182 182 182
## [32,] 243 243 243 208 182 183 182 182 182 182
## [33,] 243 243 243 220 184 182 182 182 182 182
## [34,] 218 243 243 243 182 182 181 181 181 181
## [35,] 187 182 213 208 191 182 181 181 181 181
## [36,] 183 182 182 182 182 180 180 180 181 181
## [37,] 182 181 179 179 176 177 178 179 180 181
## [38,] 182 177 173 171 171 174 176 178 180 181
## [39,] 182 173 165 164 167 170 174 177 180 182
## [40,] 182 168 156 158 161 166 171 176 182 182
## [41,] 182 161 145 144 147 156 167 173 182 182
## [42,] 182 154 134 121 133 141 155 163 171 178
## [43,] 142 142 121 123 121 131 142 151 162 168
## [44,] 126 122 123 122 122 121 131 140 154 162
## [45,] 121 121 121 121 121 121 121 129 146 156
## [46,] 121 121 121 121 121 121 121 132 145 157
## [47,] 121 121 121 121 121 121 121 155 165 168
## [48,] 121 121 121 121 133 152 172 180 182 182
## [49,] 121 121 121 121 152 182 178 182 181 182
## [50,] 121 121 121 121 151 182 182 182 182 182
## [51,] 121 121 121 121 150 182 182 182 182 182
## [52,] 121 121 121 121 145 165 182 182 182 182
## [53,] 121 121 121 121 135 162 174 178 181 182
## [54,] 121 121 121 121 121 163 175 177 179 182
## [55,] 132 125 121 121 142 168 177 179 180 182
## [56,] 141 135 132 135 167 177 180 180 181 182
## [57,] 151 147 146 147 172 179 181 181 182 182
## [58,] 162 159 160 160 176 180 181 182 182 182
## [59,] 173 172 175 171 178 180 181 182 182 182
## [60,] 180 180 181 182 179 180 181 182 182 182
## [61,] 182 182 182 182 182 182 182 182 187 182
## [62,] 182 182 182 183 182 182 182 182 200 199
## [63,] 182 182 182 186 185 182 182 182 212 213
## [64,] 182 185 190 194 197 190 182 199 235 236
## [65,] 182 190 204 214 222 218 215 222 237 243
## [66,] 182 205 226 237 243 245 238 235 239 243
## [67,] 197 215 243 241 250 253 253 243 243 243
## [68,] 197 218 238 243 257 269 280 286 279 274
## [69,] 195 215 234 243 263 281 304 301 304 304
## [70,] 196 217 235 243 260 276 291 304 304 304
## [71,] 201 225 243 251 260 272 286 304 304 304
## [72,] 208 234 242 252 260 266 277 293 304 303
## [73,] 221 236 243 248 252 255 264 277 287 299
## [74,] 227 238 243 243 245 243 253 267 280 290
## [75,] 238 241 243 243 243 237 241 249 266 284
## [76,] 242 243 243 243 243 225 232 240 243 274
## [77,] 241 243 243 223 191 206 222 240 249 264
## [78,] 230 243 202 182 189 182 213 243 249 255
## [79,] 206 191 183 185 183 182 190 222 243 244
## [80,] 187 179 178 179 180 181 182 198 222 222
## [81,] 179 170 173 175 177 180 182 197 205 201
## [82,] 176 163 166 169 173 177 180 184 187 182
## [83,] 166 155 158 162 168 175 180 182 182 184
## [,968] [,969] [,970] [,971] [,972] [,973] [,974] [,975] [,976] [,977]
## [1,] 156 164 169 173 175 176 178 179 180 182
## [2,] 157 163 167 170 172 173 174 175 177 180
## [3,] 156 159 162 164 166 167 168 169 172 176
## [4,] 150 152 153 155 156 158 159 159 163 169
## [5,] 141 143 144 145 146 148 149 149 154 162
## [6,] 132 134 135 136 137 139 139 141 147 156
## [7,] 125 126 127 128 129 130 131 134 143 153
## [8,] 122 122 123 123 124 124 126 131 141 152
## [9,] 121 121 121 121 121 121 123 128 138 150
## [10,] 121 121 121 121 121 121 122 127 137 148
## [11,] 122 121 121 121 121 121 121 125 134 145
## [12,] 124 123 122 121 121 121 121 123 131 144
## [13,] 132 127 124 123 122 121 121 121 127 140
## [14,] 143 134 133 128 125 123 122 121 124 134
## [15,] 160 156 145 139 131 128 124 123 122 130
## [16,] 175 172 162 154 147 135 132 128 125 133
## [17,] 189 184 174 168 164 156 145 138 134 143
## [18,] 202 193 185 180 178 172 160 151 146 153
## [19,] 217 203 195 191 188 183 172 163 159 162
## [20,] 229 219 209 203 199 193 183 175 170 169
## [21,] 238 232 223 216 211 204 194 187 179 176
## [22,] 243 243 238 230 225 216 207 199 185 181
## [23,] 243 243 243 243 243 232 223 217 204 182
## [24,] 231 234 241 243 243 243 238 236 233 221
## [25,] 216 219 227 243 243 243 243 243 243 243
## [26,] 202 203 208 210 218 228 236 241 243 243
## [27,] 188 185 182 182 195 207 218 229 239 243
## [28,] 183 183 182 182 182 188 206 219 236 243
## [29,] 182 182 182 182 182 191 195 208 226 243
## [30,] 182 182 182 182 182 188 192 201 216 233
## [31,] 182 182 182 182 182 182 182 188 200 226
## [32,] 182 182 182 182 182 182 182 186 196 217
## [33,] 182 182 182 182 182 182 182 182 187 211
## [34,] 181 182 182 182 182 182 182 182 182 209
## [35,] 181 181 182 182 182 182 182 186 209 225
## [36,] 181 182 182 182 182 187 189 201 221 237
## [37,] 182 182 183 185 188 194 200 215 231 243
## [38,] 182 182 184 188 193 203 212 226 243 241
## [39,] 182 182 185 191 198 208 221 232 243 243
## [40,] 182 182 188 191 195 211 232 243 241 242
## [41,] 182 182 182 182 182 207 243 243 242 243
## [42,] 180 181 181 182 182 182 193 208 213 223
## [43,] 175 179 181 182 182 182 182 182 182 182
## [44,] 171 178 180 182 182 182 182 182 182 187
## [45,] 168 177 181 182 182 182 182 182 182 182
## [46,] 171 181 183 183 182 182 182 182 182 182
## [47,] 178 183 188 189 188 182 188 190 182 182
## [48,] 182 186 193 199 201 202 210 214 208 202
## [49,] 182 188 200 210 217 221 230 243 230 221
## [50,] 182 191 210 224 236 235 240 240 243 232
## [51,] 182 182 226 243 239 243 242 243 243 243
## [52,] 182 213 243 239 242 242 243 243 245 247
## [53,] 190 212 243 243 243 243 241 243 248 255
## [54,] 192 209 222 243 210 182 220 243 252 269
## [55,] 182 189 204 200 197 182 190 224 243 265
## [56,] 182 182 182 187 182 184 182 208 226 243
## [57,] 182 182 182 182 183 182 182 201 212 222
## [58,] 182 182 182 182 182 182 182 191 197 202
## [59,] 182 182 182 182 182 182 182 182 184 185
## [60,] 182 182 182 182 182 182 182 182 182 182
## [61,] 182 182 182 182 182 182 182 182 182 182
## [62,] 195 189 182 182 182 182 182 182 182 182
## [63,] 209 202 192 182 182 182 182 182 182 182
## [64,] 227 223 210 200 189 182 182 182 182 182
## [65,] 243 243 228 214 200 185 182 182 182 182
## [66,] 256 255 248 236 221 208 199 193 192 187
## [67,] 272 274 265 255 238 229 222 219 223 210
## [68,] 295 297 285 279 265 253 240 240 242 235
## [69,] 304 304 304 304 304 304 279 250 243 243
## [70,] 304 304 304 304 304 304 304 266 248 244
## [71,] 304 304 304 304 304 304 277 263 243 245
## [72,] 304 304 304 304 304 280 268 243 250 243
## [73,] 303 304 304 304 295 270 256 251 245 244
## [74,] 301 304 304 304 277 259 251 247 245 245
## [75,] 302 303 304 285 259 251 249 246 245 244
## [76,] 288 304 282 274 249 243 245 245 243 243
## [77,] 273 275 268 257 246 243 243 243 238 242
## [78,] 256 259 256 249 245 243 243 228 232 241
## [79,] 241 246 248 246 235 223 218 216 224 243
## [80,] 228 234 243 244 215 197 182 182 205 228
## [81,] 206 212 217 216 192 186 184 182 194 218
## [82,] 187 188 182 186 190 183 182 191 202 218
## [83,] 182 184 182 183 182 185 182 197 211 222
## [,978] [,979] [,980] [,981] [,982] [,983] [,984] [,985] [,986] [,987]
## [1,] 185 188 191 193 194 194 193 193 193 193
## [2,] 183 187 190 192 192 191 190 190 191 191
## [3,] 180 184 188 190 190 188 187 188 190 190
## [4,] 175 180 184 186 186 185 185 185 187 187
## [5,] 169 176 181 183 183 183 183 183 184 185
## [6,] 165 173 179 182 182 182 183 183 184 185
## [7,] 164 173 179 182 182 182 184 185 187 189
## [8,] 163 172 178 181 182 183 186 189 193 196
## [9,] 162 171 177 181 182 184 189 195 201 205
## [10,] 160 170 177 180 182 186 194 202 211 213
## [11,] 157 167 176 180 183 188 199 210 220 221
## [12,] 157 169 176 180 183 188 195 205 223 231
## [13,] 153 166 175 180 182 184 187 193 192 200
## [14,] 147 160 172 179 182 182 183 184 187 187
## [15,] 143 157 170 178 181 182 182 182 182 182
## [16,] 146 158 169 177 181 182 182 182 182 182
## [17,] 154 164 172 178 180 182 182 182 182 182
## [18,] 162 170 175 179 181 182 182 182 182 182
## [19,] 168 173 177 180 182 182 182 182 182 182
## [20,] 172 175 178 181 182 182 182 182 182 182
## [21,] 177 178 179 182 182 183 182 182 182 182
## [22,] 181 181 181 182 183 184 182 182 182 182
## [23,] 188 182 182 182 187 188 182 182 182 182
## [24,] 209 207 197 198 198 201 195 192 191 187
## [25,] 231 229 217 224 220 218 211 212 210 204
## [26,] 243 243 237 238 235 237 227 227 228 227
## [27,] 243 243 243 243 243 243 243 240 243 243
## [28,] 243 243 243 243 243 243 243 243 242 243
## [29,] 243 243 243 243 243 243 243 243 243 243
## [30,] 243 243 243 243 243 243 243 243 243 243
## [31,] 239 243 243 243 243 243 243 243 243 243
## [32,] 231 239 243 243 243 243 243 243 243 243
## [33,] 229 242 242 243 243 243 243 243 243 243
## [34,] 232 243 243 243 243 243 243 243 243 243
## [35,] 238 241 242 243 243 243 243 243 243 243
## [36,] 239 239 243 243 243 243 243 243 243 243
## [37,] 242 243 243 243 243 243 243 243 243 243
## [38,] 243 243 243 243 243 243 243 243 243 243
## [39,] 242 243 243 244 245 243 243 243 243 243
## [40,] 243 243 243 245 250 249 245 243 243 243
## [41,] 241 243 243 247 258 259 252 243 243 243
## [42,] 235 243 243 258 288 289 271 249 243 243
## [43,] 222 243 239 274 304 304 304 262 243 243
## [44,] 201 212 226 240 274 284 269 257 250 245
## [45,] 182 197 210 234 243 243 249 247 245 245
## [46,] 182 182 190 216 239 242 243 243 243 243
## [47,] 182 182 182 203 234 238 241 242 243 243
## [48,] 196 191 192 224 234 237 240 242 242 243
## [49,] 216 214 214 228 234 237 239 242 242 243
## [50,] 229 228 226 231 235 238 241 243 243 251
## [51,] 244 243 239 236 238 242 243 243 243 260
## [52,] 248 243 243 242 242 243 245 244 243 294
## [53,] 265 267 248 243 243 250 249 247 269 296
## [54,] 289 304 276 243 267 261 255 249 257 263
## [55,] 292 302 304 304 294 270 257 249 244 238
## [56,] 262 276 304 304 281 273 253 243 228 224
## [57,] 231 238 257 255 261 250 226 212 208 206
## [58,] 201 215 218 223 243 205 182 182 191 189
## [59,] 183 190 188 184 182 182 188 183 182 182
## [60,] 182 183 182 182 183 182 182 183 182 182
## [61,] 182 182 182 182 182 182 182 182 182 182
## [62,] 182 182 182 182 182 182 182 182 182 182
## [63,] 182 182 182 182 182 182 182 182 182 182
## [64,] 182 182 182 182 182 182 182 182 182 197
## [65,] 182 182 182 182 182 182 182 182 182 199
## [66,] 182 182 182 182 182 182 182 182 182 192
## [67,] 198 182 182 182 182 182 182 182 182 182
## [68,] 231 197 182 182 182 182 182 182 182 182
## [69,] 227 216 204 200 202 198 196 186 182 182
## [70,] 239 231 218 218 222 214 211 203 202 202
## [71,] 243 242 237 239 243 236 231 227 233 233
## [72,] 244 243 243 244 243 243 243 242 255 263
## [73,] 243 243 247 250 252 251 251 262 281 293
## [74,] 243 243 251 258 266 272 275 287 304 300
## [75,] 243 243 255 268 284 296 298 301 302 304
## [76,] 243 243 255 274 304 301 304 304 303 304
## [77,] 243 243 243 252 259 285 289 288 296 296
## [78,] 243 243 243 243 243 243 243 252 277 277
## [79,] 243 243 243 243 243 243 243 248 261 264
## [80,] 243 243 243 243 243 243 243 251 251 251
## [81,] 239 243 243 243 243 243 243 243 246 246
## [82,] 234 243 243 243 243 243 243 243 243 243
## [83,] 239 242 243 243 243 243 243 243 243 243
## [,988] [,989] [,990] [,991] [,992] [,993] [,994] [,995] [,996] [,997]
## [1,] 192 191 191 191 191 190 189 190 196 206
## [2,] 190 188 187 187 187 188 188 192 206 230
## [3,] 188 186 185 185 185 187 188 196 221 260
## [4,] 185 184 183 183 184 186 187 195 220 259
## [5,] 184 183 182 182 184 186 188 197 221 254
## [6,] 185 184 183 183 186 189 193 197 211 220
## [7,] 189 187 186 186 189 195 201 205 210 217
## [8,] 196 192 190 191 196 204 211 215 218 221
## [9,] 206 200 196 197 204 213 220 225 227 229
## [10,] 215 208 201 203 212 220 227 232 235 236
## [11,] 223 213 204 206 214 223 231 236 239 240
## [12,] 223 207 199 201 208 220 231 237 241 242
## [13,] 208 197 192 193 199 210 222 233 239 242
## [14,] 192 189 185 185 190 201 214 228 237 241
## [15,] 184 183 182 182 183 192 208 225 236 240
## [16,] 182 182 182 182 182 185 195 214 228 237
## [17,] 182 182 182 182 183 183 187 199 218 231
## [18,] 182 182 183 186 188 186 185 199 217 230
## [19,] 182 183 189 196 200 192 198 208 219 230
## [20,] 182 187 198 208 213 213 218 223 229 236
## [21,] 183 194 210 221 228 232 239 240 240 241
## [22,] 182 193 226 241 243 248 258 258 250 243
## [23,] 182 182 224 243 242 259 273 274 266 254
## [24,] 182 197 228 240 254 272 288 289 284 273
## [25,] 205 218 243 259 274 288 304 304 302 291
## [26,] 230 242 254 273 289 297 298 304 304 304
## [27,] 243 252 273 296 302 304 303 303 298 304
## [28,] 243 251 275 286 304 304 304 304 283 289
## [29,] 243 248 262 270 276 281 274 250 268 278
## [30,] 243 243 246 248 243 243 249 244 257 268
## [31,] 243 243 243 243 244 243 243 247 247 258
## [32,] 243 243 243 243 243 246 243 252 245 243
## [33,] 243 246 249 254 260 259 243 260 245 244
## [34,] 246 254 267 280 304 304 304 268 245 244
## [35,] 247 257 266 277 295 304 304 270 244 243
## [36,] 243 243 255 260 274 275 272 253 243 243
## [37,] 243 243 243 243 259 255 254 243 243 243
## [38,] 243 243 243 243 243 243 243 243 243 243
## [39,] 243 243 243 243 243 243 243 243 243 243
## [40,] 243 243 243 243 243 243 243 243 243 243
## [41,] 243 243 243 243 243 243 243 243 243 243
## [42,] 243 243 243 243 243 243 243 243 243 243
## [43,] 243 243 243 243 243 243 243 243 243 243
## [44,] 243 243 243 243 243 243 243 243 243 243
## [45,] 243 243 243 243 243 243 243 243 243 243
## [46,] 243 244 244 244 243 243 243 243 243 243
## [47,] 243 245 245 245 243 243 243 243 243 243
## [48,] 243 245 246 246 243 243 243 243 243 243
## [49,] 248 251 252 251 248 243 243 243 252 270
## [50,] 263 267 265 262 259 252 243 267 272 282
## [51,] 293 294 285 279 274 275 276 294 297 299
## [52,] 304 304 304 295 291 293 304 301 304 304
## [53,] 294 291 291 291 290 294 297 297 293 278
## [54,] 267 260 267 273 275 277 275 274 266 256
## [55,] 237 240 249 254 257 258 257 254 248 244
## [56,] 220 225 232 243 243 243 243 243 232 236
## [57,] 201 206 209 216 221 221 228 223 223 229
## [58,] 182 187 182 195 200 200 205 202 210 217
## [59,] 184 182 184 182 188 185 182 182 194 204
## [60,] 182 182 182 182 182 183 183 182 182 188
## [61,] 182 182 182 182 182 182 182 182 190 199
## [62,] 182 182 182 182 189 190 191 200 202 210
## [63,] 193 202 202 209 211 213 212 215 217 221
## [64,] 210 232 233 235 235 236 228 229 230 230
## [65,] 216 227 243 243 243 243 243 243 243 239
## [66,] 205 216 228 239 243 243 243 243 243 243
## [67,] 192 202 217 228 238 243 243 243 243 243
## [68,] 182 187 207 220 232 242 243 243 243 260
## [69,] 182 200 205 217 234 243 243 256 269 278
## [70,] 209 210 219 222 233 241 243 272 289 304
## [71,] 235 235 236 234 238 254 273 294 302 302
## [72,] 263 259 252 243 250 271 286 292 304 303
## [73,] 294 283 277 270 271 280 289 296 300 304
## [74,] 304 304 304 289 289 293 295 299 304 302
## [75,] 304 304 304 303 301 304 304 304 304 304
## [76,] 304 304 304 304 304 304 304 304 304 304
## [77,] 297 301 304 298 302 304 304 304 304 304
## [78,] 281 287 284 284 293 301 304 304 304 304
## [79,] 266 269 273 275 287 298 302 304 304 304
## [80,] 251 251 255 260 281 301 303 304 304 304
## [81,] 246 246 243 244 263 286 304 304 304 304
## [82,] 243 243 243 243 248 268 281 296 304 287
## [83,] 243 243 243 242 243 255 259 269 269 263
## [,998] [,999] [,1000] [,1001] [,1002] [,1003] [,1004] [,1005] [,1006]
## [1,] 205 196 192 185 184 185 189 193 196
## [2,] 240 229 218 208 202 199 200 200 200
## [3,] 268 257 244 232 220 214 212 210 209
## [4,] 273 265 253 242 232 228 224 222 219
## [5,] 263 259 256 248 240 237 234 231 227
## [6,] 230 243 246 243 241 241 238 235 230
## [7,] 223 230 237 236 236 236 234 232 228
## [8,] 224 228 230 232 232 231 229 227 224
## [9,] 230 232 233 233 232 230 226 222 219
## [10,] 237 238 238 238 236 231 225 219 214
## [11,] 241 242 242 241 238 230 221 214 209
## [12,] 243 243 243 243 239 226 214 208 209
## [13,] 243 243 243 243 240 229 223 219 220
## [14,] 243 243 243 243 243 238 233 230 230
## [15,] 242 243 243 243 243 243 241 238 239
## [16,] 241 243 243 243 243 243 243 243 243
## [17,] 239 242 243 243 243 243 244 246 245
## [18,] 238 242 243 243 243 245 251 253 249
## [19,] 239 242 243 243 244 251 261 266 255
## [20,] 241 243 243 243 246 261 276 281 273
## [21,] 242 242 243 243 248 274 286 293 290
## [22,] 243 243 243 243 243 261 282 297 303
## [23,] 243 243 243 243 243 249 270 287 300
## [24,] 261 249 243 243 243 243 260 286 304
## [25,] 280 267 256 243 243 243 260 287 297
## [26,] 292 278 269 268 271 280 285 298 300
## [27,] 302 296 290 291 300 304 302 303 304
## [28,] 296 298 300 301 303 303 304 304 304
## [29,] 285 292 299 302 304 304 304 304 304
## [30,] 279 288 299 304 304 304 304 304 304
## [31,] 270 280 296 304 304 304 304 304 304
## [32,] 255 260 274 290 304 304 304 304 304
## [33,] 243 243 251 271 290 304 293 288 293
## [34,] 243 243 243 253 266 270 267 256 243
## [35,] 243 243 243 243 249 252 243 243 182
## [36,] 243 243 243 243 243 229 182 190 204
## [37,] 243 243 243 243 243 217 202 182 182
## [38,] 243 243 243 243 243 224 213 210 200
## [39,] 243 243 243 243 243 234 228 229 225
## [40,] 243 253 274 256 249 243 242 252 249
## [41,] 243 243 304 295 279 272 280 280 278
## [42,] 246 274 297 304 304 300 303 304 310
## [43,] 252 274 291 302 304 304 304 304 311
## [44,] 256 276 299 303 303 304 304 294 288
## [45,] 243 276 292 304 304 304 304 274 243
## [46,] 243 272 295 304 304 304 304 275 243
## [47,] 243 294 302 303 304 304 304 284 253
## [48,] 275 304 304 304 303 304 304 304 268
## [49,] 284 300 304 304 304 304 304 287 269
## [50,] 292 304 302 304 304 304 304 294 270
## [51,] 302 295 302 300 302 304 304 295 276
## [52,] 281 285 289 289 291 291 285 278 265
## [53,] 263 267 276 275 277 274 268 258 247
## [54,] 243 252 264 263 263 263 259 243 244
## [55,] 244 243 255 260 263 267 271 270 244
## [56,] 239 242 249 264 273 282 293 304 267
## [57,] 235 239 247 264 276 288 304 300 300
## [58,] 226 238 245 258 271 286 299 304 304
## [59,] 217 233 243 252 261 280 291 299 304
## [60,] 208 227 239 243 248 274 287 297 303
## [61,] 203 223 239 243 256 270 284 297 303
## [62,] 217 228 241 243 253 269 285 301 304
## [63,] 226 233 239 242 243 268 286 296 304
## [64,] 232 236 242 249 262 274 288 301 304
## [65,] 239 240 243 262 275 288 304 303 303
## [66,] 247 251 265 274 285 299 304 304 304
## [67,] 258 270 286 288 294 304 304 304 304
## [68,] 267 283 304 297 299 304 306 305 304
## [69,] 288 295 313 320 318 314 311 306 304
## [70,] 304 304 345 365 350 339 325 312 304
## [71,] 304 316 351 362 365 359 339 319 307
## [72,] 304 320 339 365 365 347 341 319 304
## [73,] 304 309 314 328 334 331 326 315 305
## [74,] 304 304 304 304 315 314 320 319 311
## [75,] 304 304 304 304 304 307 334 328 321
## [76,] 304 304 304 304 304 304 365 346 340
## [77,] 304 304 304 304 304 304 348 365 365
## [78,] 304 304 304 304 303 304 330 352 340
## [79,] 304 304 304 304 301 302 304 320 322
## [80,] 304 304 298 297 296 299 310 310 310
## [81,] 295 289 282 281 280 286 300 308 309
## [82,] 279 273 266 260 253 267 285 304 305
## [83,] 262 259 253 243 246 243 267 288 304
## [,1007] [,1008] [,1009] [,1010] [,1011] [,1012] [,1013] [,1014] [,1015]
## [1,] 199 200 200 199 207 198 179 159 142
## [2,] 201 202 204 211 229 221 197 168 146
## [3,] 206 205 207 219 238 224 193 161 136
## [4,] 214 211 210 219 239 227 197 166 142
## [5,] 220 215 211 207 218 203 179 156 137
## [6,] 222 214 206 196 174 154 142 133 126
## [7,] 221 213 204 187 163 145 134 128 123
## [8,] 218 211 199 182 157 140 131 126 123
## [9,] 214 208 198 183 160 144 136 131 127
## [10,] 209 205 201 190 168 153 146 140 134
## [11,] 207 208 212 206 189 173 161 152 144
## [12,] 212 218 226 225 211 197 179 166 156
## [13,] 221 232 235 235 219 201 183 172 165
## [14,] 232 237 239 229 214 198 188 179 174
## [15,] 240 241 238 221 202 193 187 183 181
## [16,] 243 241 231 214 198 189 186 185 185
## [17,] 244 240 227 205 197 192 193 193 196
## [18,] 246 243 232 219 207 203 206 209 206
## [19,] 252 246 240 231 226 220 223 233 226
## [20,] 262 257 251 244 242 239 240 242 239
## [21,] 281 275 264 254 258 259 255 252 249
## [22,] 299 296 284 274 275 279 268 261 256
## [23,] 304 304 302 296 296 304 278 269 263
## [24,] 303 304 304 302 304 304 283 276 269
## [25,] 302 303 304 304 304 291 287 281 275
## [26,] 301 302 304 304 304 299 293 285 274
## [27,] 304 304 304 304 304 304 301 289 274
## [28,] 304 304 304 304 304 304 304 291 271
## [29,] 304 304 304 304 304 304 304 281 258
## [30,] 304 304 303 304 304 304 276 263 239
## [31,] 304 299 295 297 291 273 253 236 203
## [32,] 304 293 280 277 268 258 243 218 184
## [33,] 304 263 262 258 260 253 243 228 195
## [34,] 243 213 243 243 249 247 246 244 222
## [35,] 232 216 182 182 243 243 243 244 237
## [36,] 209 204 187 183 183 182 203 230 238
## [37,] 195 190 184 184 183 181 181 192 225
## [38,] 192 187 183 183 182 180 178 179 191
## [39,] 216 205 189 182 182 178 174 170 164
## [40,] 237 226 204 189 182 175 168 158 144
## [41,] 293 253 224 205 182 177 167 153 138
## [42,] 316 287 253 233 201 182 174 161 149
## [43,] 307 304 273 243 208 190 182 172 165
## [44,] 301 304 270 243 202 182 186 181 178
## [45,] 268 275 260 238 182 184 183 188 201
## [46,] 248 253 243 215 182 182 182 203 243
## [47,] 243 245 230 206 182 182 182 213 241
## [48,] 239 216 202 182 191 183 200 223 243
## [49,] 236 210 182 184 183 184 208 241 241
## [50,] 250 225 200 182 182 182 182 243 243
## [51,] 254 243 210 182 182 182 182 192 223
## [52,] 249 228 216 203 182 182 182 182 182
## [53,] 245 233 224 220 205 189 182 182 182
## [54,] 244 243 241 243 224 205 182 182 182
## [55,] 243 251 243 248 243 223 191 182 182
## [56,] 270 279 293 268 244 238 211 197 206
## [57,] 295 304 299 304 274 243 228 226 228
## [58,] 304 303 304 303 304 275 247 238 240
## [59,] 304 304 304 305 304 284 260 243 262
## [60,] 304 304 304 308 309 302 282 281 287
## [61,] 304 304 308 313 316 315 304 298 322
## [62,] 304 306 313 319 326 334 338 335 355
## [63,] 304 308 315 324 333 350 365 363 365
## [64,] 304 307 308 320 332 356 364 365 364
## [65,] 304 304 304 304 318 340 365 347 352
## [66,] 304 304 304 304 304 324 325 328 321
## [67,] 304 304 304 304 304 305 305 304 304
## [68,] 304 304 304 303 304 304 304 305 304
## [69,] 304 304 303 303 303 304 304 311 327
## [70,] 304 304 302 301 302 304 314 328 350
## [71,] 304 302 298 293 297 304 317 330 346
## [72,] 301 295 286 277 283 296 304 308 304
## [73,] 297 283 266 252 267 284 294 302 305
## [74,] 304 274 243 248 251 273 287 300 304
## [75,] 309 294 256 243 245 263 285 304 303
## [76,] 318 304 277 243 243 243 270 296 304
## [77,] 325 304 284 243 243 243 243 278 304
## [78,] 328 315 304 258 243 243 249 267 287
## [79,] 321 313 304 274 243 243 252 266 283
## [80,] 311 309 304 275 243 243 243 250 280
## [81,] 306 306 304 280 252 243 243 243 274
## [82,] 305 305 304 277 243 243 243 258 277
## [83,] 304 304 304 287 243 243 243 243 274
## [,1016] [,1017] [,1018] [,1019] [,1020] [,1021] [,1022] [,1023] [,1024]
## [1,] 127 116 109 108 109 112 116 120 124
## [2,] 129 117 108 106 107 110 114 118 123
## [3,] 121 112 107 105 106 108 113 118 121
## [4,] 125 114 107 105 105 107 111 115 117
## [5,] 123 113 108 106 105 106 108 110 111
## [6,] 119 113 109 107 106 105 105 105 104
## [7,] 118 114 111 109 107 105 103 100 96
## [8,] 120 117 113 111 109 107 104 97 91
## [9,] 124 120 117 115 113 112 107 97 88
## [10,] 130 125 122 120 119 117 111 101 89
## [11,] 139 132 126 123 121 120 115 105 94
## [12,] 148 139 132 127 123 121 119 111 99
## [13,] 160 152 142 132 126 122 119 109 99
## [14,] 171 166 155 142 131 124 120 110 99
## [15,] 180 176 166 150 135 127 125 114 103
## [16,] 184 182 170 149 135 132 139 129 117
## [17,] 189 184 174 160 141 149 165 160 141
## [18,] 195 188 181 173 167 174 178 179 170
## [19,] 210 197 191 188 187 186 189 188 184
## [20,] 226 216 206 205 205 199 198 193 188
## [21,] 241 233 225 224 220 212 205 194 190
## [22,] 249 243 243 243 234 225 214 208 196
## [23,] 255 249 246 244 243 239 232 234 219
## [24,] 260 253 249 245 243 242 242 243 243
## [25,] 265 256 251 246 243 240 240 243 243
## [26,] 264 257 252 247 243 231 220 243 243
## [27,] 263 256 251 245 238 216 188 199 228
## [28,] 259 254 249 246 243 214 182 183 182
## [29,] 253 251 248 245 244 236 185 179 179
## [30,] 243 246 246 245 243 182 186 176 174
## [31,] 186 213 244 232 212 199 181 173 170
## [32,] 183 185 182 206 195 181 173 168 164
## [33,] 183 182 183 182 182 180 169 162 156
## [34,] 190 182 182 182 182 176 165 157 149
## [35,] 207 196 182 182 182 174 161 151 141
## [36,] 218 218 216 201 186 176 163 151 138
## [37,] 224 243 243 227 194 184 173 157 143
## [38,] 195 199 213 213 187 183 174 161 148
## [39,] 159 142 121 152 152 158 157 149 144
## [40,] 128 123 125 122 121 130 133 133 132
## [41,] 121 121 122 121 122 122 121 121 123
## [42,] 142 130 121 121 121 124 129 125 121
## [43,] 164 159 140 121 121 131 141 135 126
## [44,] 182 182 161 148 121 149 154 144 128
## [45,] 209 200 192 186 164 167 143 152 126
## [46,] 243 226 216 205 196 182 121 159 121
## [47,] 242 243 237 225 219 179 156 175 172
## [48,] 243 243 243 243 243 215 207 198 182
## [49,] 243 243 243 243 243 243 227 213 201
## [50,] 243 243 243 243 243 243 236 226 212
## [51,] 236 243 243 243 243 246 245 238 226
## [52,] 202 224 238 243 243 251 255 250 243
## [53,] 182 211 234 243 245 256 264 258 250
## [54,] 204 217 238 250 262 276 290 276 263
## [55,] 206 225 243 261 285 304 302 304 284
## [56,] 217 231 240 267 299 309 315 313 308
## [57,] 232 243 262 291 311 321 329 329 321
## [58,] 250 262 275 297 326 339 352 353 339
## [59,] 269 281 292 314 340 365 362 365 365
## [60,] 289 298 312 332 352 361 364 364 365
## [61,] 302 304 333 356 365 363 365 364 365
## [62,] 335 355 355 361 364 365 365 365 365
## [63,] 360 365 365 365 365 364 365 365 365
## [64,] 365 364 365 365 365 365 365 365 365
## [65,] 351 358 365 365 365 365 365 365 365
## [66,] 323 329 345 365 365 365 365 365 365
## [67,] 304 304 333 359 364 365 365 365 365
## [68,] 317 326 345 365 365 364 365 365 371
## [69,] 339 347 361 364 364 365 365 370 379
## [70,] 365 365 364 365 365 365 365 374 386
## [71,] 359 365 364 365 365 365 365 364 377
## [72,] 325 342 359 365 365 365 365 361 363
## [73,] 304 329 356 364 365 365 357 351 354
## [74,] 319 329 356 365 365 365 340 321 339
## [75,] 319 336 357 365 365 365 333 304 318
## [76,] 320 339 362 365 365 351 328 304 309
## [77,] 316 352 365 365 337 324 304 313 305
## [78,] 304 334 346 332 314 306 307 305 304
## [79,] 304 318 319 312 304 304 305 304 300
## [80,] 301 304 308 305 305 304 304 304 293
## [81,] 304 304 304 304 305 304 304 304 286
## [82,] 304 304 304 304 304 304 304 297 275
## [83,] 288 304 304 304 304 304 304 277 256
## [,1025] [,1026] [,1027] [,1028] [,1029] [,1030] [,1031] [,1032] [,1033]
## [1,] 127 129 132 135 137 138 137 133 126
## [2,] 126 128 132 137 139 140 139 136 130
## [3,] 124 126 131 135 139 141 140 137 131
## [4,] 119 120 125 130 135 137 137 136 131
## [5,] 112 112 116 122 128 132 133 132 128
## [6,] 102 102 106 113 119 125 127 127 126
## [7,] 93 92 96 102 109 117 122 124 124
## [8,] 85 83 85 91 100 109 116 120 121
## [9,] 80 75 75 81 91 102 109 114 117
## [10,] 79 72 69 74 85 92 98 105 110
## [11,] 82 72 66 67 75 81 87 94 101
## [12,] 86 73 66 63 65 70 71 81 91
## [13,] 88 77 67 63 62 62 62 70 73
## [14,] 89 77 68 63 61 60 60 62 62
## [15,] 91 76 71 65 62 61 60 60 60
## [16,] 105 94 82 71 66 63 61 60 60
## [17,] 126 115 106 89 74 70 64 62 61
## [18,] 159 140 131 117 98 83 71 68 65
## [19,] 172 173 156 140 124 107 91 76 76
## [20,] 183 178 167 151 136 121 108 96 92
## [21,] 184 180 170 157 142 131 121 111 113
## [22,] 182 182 176 170 149 121 131 121 121
## [23,] 203 191 189 185 171 152 162 152 172
## [24,] 222 212 209 200 190 185 183 183 182
## [25,] 238 228 226 217 200 189 185 183 182
## [26,] 243 243 243 233 206 190 185 183 183
## [27,] 243 243 243 234 204 185 183 182 182
## [28,] 213 243 243 211 182 185 183 183 182
## [29,] 180 181 194 194 188 184 183 182 182
## [30,] 174 176 179 182 183 183 183 182 182
## [31,] 170 172 174 178 182 182 182 182 182
## [32,] 164 165 167 171 178 182 182 182 182
## [33,] 158 158 159 165 173 182 182 182 179
## [34,] 146 144 144 152 162 169 172 165 167
## [35,] 130 121 121 136 148 154 153 150 152
## [36,] 126 122 122 124 135 138 137 137 136
## [37,] 133 127 121 121 121 121 121 125 121
## [38,] 137 128 121 121 121 121 121 121 122
## [39,] 136 128 121 121 121 121 121 121 121
## [40,] 129 125 123 121 121 121 121 121 121
## [41,] 123 123 122 122 121 121 121 121 121
## [42,] 121 122 122 121 121 121 121 121 121
## [43,] 123 122 121 121 121 121 121 121 121
## [44,] 124 122 121 121 121 121 121 121 121
## [45,] 122 122 121 121 121 121 121 121 121
## [46,] 121 121 121 121 121 121 121 121 121
## [47,] 148 130 121 121 121 121 121 121 123
## [48,] 182 162 128 121 121 121 121 126 143
## [49,] 189 173 130 121 121 121 121 126 167
## [50,] 198 172 121 121 121 121 121 151 181
## [51,] 211 189 155 121 121 121 121 149 174
## [52,] 229 204 182 182 121 121 121 145 167
## [53,] 243 217 203 191 182 121 158 154 167
## [54,] 249 237 224 217 209 195 187 177 174
## [55,] 266 248 243 243 243 226 211 195 181
## [56,] 294 292 290 263 251 245 235 207 182
## [57,] 313 304 287 276 261 249 244 227 196
## [58,] 325 307 294 279 263 246 244 225 208
## [59,] 344 321 304 284 266 243 243 231 219
## [60,] 356 329 310 299 279 267 252 239 237
## [61,] 361 340 321 304 294 288 281 265 257
## [62,] 365 349 330 304 304 304 304 282 270
## [63,] 365 365 355 349 325 323 317 303 288
## [64,] 366 366 365 366 365 346 338 322 304
## [65,] 367 369 368 368 366 361 359 343 322
## [66,] 369 372 372 372 370 366 365 365 338
## [67,] 371 377 378 378 377 366 365 354 344
## [68,] 379 387 391 395 399 381 365 359 350
## [69,] 396 408 412 420 426 406 378 366 361
## [70,] 414 426 423 420 426 426 384 367 366
## [71,] 409 426 418 410 407 398 378 364 365
## [72,] 385 385 392 380 365 373 359 349 353
## [73,] 365 365 372 365 363 365 345 333 331
## [74,] 365 365 365 349 336 333 325 310 306
## [75,] 365 365 365 334 304 313 308 309 304
## [76,] 352 365 352 330 304 304 304 304 304
## [77,] 325 329 332 316 304 302 302 303 304
## [78,] 310 311 308 300 297 299 301 303 304
## [79,] 300 304 292 287 291 295 299 302 304
## [80,] 289 282 277 275 280 289 297 301 304
## [81,] 275 266 262 263 271 284 296 301 303
## [82,] 259 249 248 253 265 282 297 302 303
## [83,] 243 246 243 243 263 285 301 303 304
## [,1034] [,1035] [,1036] [,1037] [,1038] [,1039] [,1040] [,1041] [,1042]
## [1,] 117 106 95 82 71 61 53 48 45
## [2,] 121 111 99 86 75 65 57 53 51
## [3,] 122 110 97 85 75 66 60 57 56
## [4,] 121 108 95 84 74 66 61 58 57
## [5,] 120 109 97 85 75 67 62 59 57
## [6,] 120 110 98 86 76 68 63 59 57
## [7,] 119 110 99 88 78 70 63 59 57
## [8,] 119 113 104 93 81 71 64 60 58
## [9,] 118 115 106 95 83 73 65 60 58
## [10,] 115 116 109 98 85 74 65 60 58
## [11,] 109 115 108 97 84 73 65 60 58
## [12,] 105 109 108 92 76 67 62 60 59
## [13,] 80 90 77 67 68 63 60 59 59
## [14,] 66 67 69 64 62 60 59 59 59
## [15,] 60 63 62 61 60 60 60 60 60
## [16,] 60 61 61 61 60 62 62 62 60
## [17,] 62 64 64 63 64 73 72 74 75
## [18,] 72 76 74 70 77 87 92 94 89
## [19,] 86 92 93 99 103 114 119 120 115
## [20,] 106 111 115 124 136 144 146 147 155
## [21,] 123 131 139 150 162 173 174 174 182
## [22,] 150 150 157 166 182 179 182 182 182
## [23,] 174 169 165 169 182 182 182 182 182
## [24,] 175 176 162 158 165 182 182 182 182
## [25,] 182 160 143 131 134 153 174 182 182
## [26,] 182 146 121 125 122 121 149 182 182
## [27,] 168 136 123 122 122 121 121 152 162
## [28,] 182 158 121 121 121 121 121 121 121
## [29,] 182 182 121 121 121 121 121 121 121
## [30,] 182 174 158 137 121 121 121 121 121
## [31,] 182 182 182 182 152 121 121 121 121
## [32,] 182 182 182 182 182 171 146 128 122
## [33,] 182 182 182 182 182 182 163 137 123
## [34,] 172 182 182 182 182 182 169 136 122
## [35,] 159 172 182 177 182 182 182 141 121
## [36,] 143 155 155 158 168 172 160 143 129
## [37,] 126 138 138 136 150 152 148 141 129
## [38,] 121 123 124 121 135 136 136 133 128
## [39,] 121 121 121 121 121 125 126 127 125
## [40,] 121 121 121 121 121 121 123 124 123
## [41,] 121 121 121 121 121 121 121 122 122
## [42,] 121 121 121 121 121 121 121 121 121
## [43,] 121 121 121 121 121 121 121 121 121
## [44,] 121 121 121 121 121 121 121 121 121
## [45,] 121 121 121 121 121 121 121 121 121
## [46,] 121 121 121 121 121 121 121 121 121
## [47,] 133 135 131 131 126 121 121 121 121
## [48,] 162 163 158 162 149 137 121 121 121
## [49,] 180 182 179 182 174 170 141 127 121
## [50,] 182 181 183 185 186 186 168 148 142
## [51,] 182 182 184 187 191 191 182 170 161
## [52,] 182 182 186 192 200 206 198 188 177
## [53,] 177 182 188 197 209 224 217 206 193
## [54,] 178 181 186 202 220 239 237 225 210
## [55,] 180 181 182 194 224 243 242 243 225
## [56,] 182 181 182 182 235 241 243 243 239
## [57,] 182 182 182 182 243 242 243 243 243
## [58,] 196 182 182 182 219 243 243 243 243
## [59,] 211 198 182 215 243 240 244 241 240
## [60,] 235 220 224 228 243 243 245 239 236
## [61,] 249 243 238 243 245 246 246 241 235
## [62,] 261 252 243 255 251 250 249 247 243
## [63,] 278 271 269 270 264 261 259 257 249
## [64,] 294 291 285 284 279 277 276 275 269
## [65,] 310 304 300 296 294 297 297 297 295
## [66,] 320 304 304 304 304 305 307 306 306
## [67,] 332 321 310 304 304 310 311 309 308
## [68,] 344 335 325 315 311 315 315 313 310
## [69,] 360 350 340 329 327 323 321 317 313
## [70,] 365 365 355 345 340 334 333 327 320
## [71,] 365 365 365 355 350 346 347 338 329
## [72,] 365 365 365 365 362 362 369 358 344
## [73,] 348 365 365 365 365 384 396 388 365
## [74,] 315 339 358 365 383 400 426 426 410
## [75,] 304 316 338 360 375 398 412 426 426
## [76,] 304 304 325 351 365 390 402 411 419
## [77,] 304 304 324 350 365 384 392 398 405
## [78,] 304 321 336 361 371 377 381 382 387
## [79,] 304 319 335 357 364 367 368 365 365
## [80,] 304 309 321 338 353 355 352 354 356
## [81,] 304 304 304 319 323 324 321 326 331
## [82,] 304 304 304 304 304 304 304 304 304
## [83,] 304 304 304 304 304 304 304 304 309
## [,1043] [,1044] [,1045] [,1046] [,1047] [,1048] [,1049] [,1050] [,1051]
## [1,] 43 42 42 43 45 48 51 56 60
## [2,] 50 49 49 51 52 54 57 61 65
## [3,] 55 55 55 57 58 59 62 66 69
## [4,] 57 56 56 58 59 60 63 67 69
## [5,] 57 56 57 58 59 60 62 66 67
## [6,] 57 56 57 58 59 60 61 64 65
## [7,] 57 57 58 58 59 60 60 61 62
## [8,] 58 58 58 59 59 60 60 60 61
## [9,] 58 59 59 59 59 60 60 60 60
## [10,] 58 59 59 59 60 60 60 60 60
## [11,] 58 59 59 59 60 60 60 60 60
## [12,] 59 59 59 59 60 60 60 60 60
## [13,] 59 59 59 59 60 60 60 60 60
## [14,] 59 60 60 60 60 60 60 60 60
## [15,] 60 60 60 60 60 60 60 60 60
## [16,] 60 69 64 60 60 60 60 60 60
## [17,] 84 97 84 69 60 60 60 60 60
## [18,] 103 121 99 78 60 60 60 60 60
## [19,] 124 124 121 97 71 60 60 60 60
## [20,] 144 143 132 121 96 60 60 60 60
## [21,] 174 172 154 129 121 87 60 60 60
## [22,] 182 182 182 121 113 93 60 60 60
## [23,] 182 182 168 145 126 110 66 60 60
## [24,] 182 175 156 132 121 106 84 60 60
## [25,] 182 176 146 127 122 109 77 60 60
## [26,] 182 157 145 131 124 121 75 60 61
## [27,] 154 146 140 129 121 104 60 67 62
## [28,] 121 121 127 121 107 81 62 61 62
## [29,] 121 121 121 117 102 80 60 62 61
## [30,] 121 121 121 114 105 87 69 60 60
## [31,] 121 121 121 116 111 94 73 60 60
## [32,] 121 121 121 121 121 105 80 67 60
## [33,] 121 121 121 121 121 106 90 81 72
## [34,] 122 121 121 121 121 110 102 96 90
## [35,] 121 121 121 121 121 120 116 113 111
## [36,] 121 121 121 121 121 121 121 119 119
## [37,] 121 121 121 121 121 121 121 121 121
## [38,] 121 121 121 121 121 121 121 121 121
## [39,] 121 121 121 121 121 121 121 121 121
## [40,] 121 121 121 121 121 121 121 121 121
## [41,] 121 121 121 121 121 121 121 121 121
## [42,] 121 121 121 121 121 121 121 121 121
## [43,] 121 121 121 121 121 121 121 121 121
## [44,] 121 121 121 121 121 121 121 121 121
## [45,] 121 121 121 121 121 121 121 121 121
## [46,] 121 121 121 121 121 121 121 121 121
## [47,] 121 121 123 122 121 121 121 121 121
## [48,] 121 121 126 125 123 121 121 121 121
## [49,] 121 131 130 127 124 122 121 121 121
## [50,] 142 138 136 131 125 122 121 121 121
## [51,] 156 150 144 137 127 123 121 121 121
## [52,] 169 160 153 144 127 122 122 121 121
## [53,] 182 171 164 155 121 123 121 121 121
## [54,] 200 188 180 183 167 137 122 121 121
## [55,] 217 206 199 188 183 182 182 131 121
## [56,] 237 225 209 192 183 182 163 148 129
## [57,] 243 243 205 182 183 182 165 151 142
## [58,] 243 230 199 182 182 182 168 157 149
## [59,] 240 243 199 182 182 182 174 167 163
## [60,] 235 243 198 182 182 182 182 180 178
## [61,] 232 195 182 183 183 182 182 182 182
## [62,] 224 219 193 182 182 182 182 182 182
## [63,] 238 232 224 197 182 182 182 182 192
## [64,] 259 243 245 223 201 182 182 182 221
## [65,] 292 278 257 243 224 210 202 219 241
## [66,] 305 304 272 243 243 238 235 243 241
## [67,] 306 305 288 243 243 243 242 241 245
## [68,] 307 305 277 262 243 243 243 243 248
## [69,] 309 297 281 272 258 243 243 243 262
## [70,] 313 301 291 287 276 270 260 269 289
## [71,] 319 308 301 299 298 304 295 294 301
## [72,] 331 311 304 304 310 310 306 303 304
## [73,] 350 328 304 323 324 324 316 308 304
## [74,] 380 350 342 344 339 338 326 308 305
## [75,] 426 377 365 365 361 365 338 305 304
## [76,] 416 414 411 391 381 379 372 337 315
## [77,] 413 425 426 426 412 408 401 374 348
## [78,] 397 415 426 428 431 427 426 412 377
## [79,] 385 404 415 426 427 428 426 426 411
## [80,] 371 393 403 414 426 426 426 426 426
## [81,] 357 375 382 387 396 381 381 406 381
## [82,] 341 365 366 365 366 365 365 372 371
## [83,] 318 342 356 360 363 365 365 367 368
## [,1052] [,1053] [,1054] [,1055] [,1056] [,1057] [,1058] [,1059] [,1060]
## [1,] 62 63 62 60 58 55 52 49 46
## [2,] 67 66 64 61 58 55 52 50 47
## [3,] 69 68 65 62 58 55 53 51 48
## [4,] 69 68 65 62 60 57 54 53 50
## [5,] 67 66 64 62 61 59 56 55 52
## [6,] 64 64 63 61 60 59 58 57 55
## [7,] 62 62 61 61 60 60 60 59 59
## [8,] 61 61 61 61 60 60 60 60 60
## [9,] 60 60 60 60 60 60 60 60 60
## [10,] 60 60 60 60 60 60 60 60 60
## [11,] 60 60 60 60 60 60 60 60 60
## [12,] 60 60 60 60 60 60 60 60 61
## [13,] 60 60 60 60 60 60 60 60 62
## [14,] 60 60 60 60 60 60 60 60 63
## [15,] 60 60 60 60 60 60 60 60 65
## [16,] 60 60 60 60 60 60 60 60 68
## [17,] 60 60 60 60 60 60 60 60 66
## [18,] 60 60 60 60 60 60 60 60 60
## [19,] 60 60 60 60 60 60 60 60 60
## [20,] 60 60 60 60 60 60 60 60 60
## [21,] 60 60 60 60 60 60 60 60 60
## [22,] 60 60 60 60 60 60 60 60 60
## [23,] 60 60 60 60 60 69 67 60 60
## [24,] 60 60 60 60 77 88 94 85 70
## [25,] 60 60 60 63 85 106 121 104 89
## [26,] 61 60 60 60 94 114 119 121 113
## [27,] 61 60 60 60 93 109 115 121 111
## [28,] 62 61 60 65 96 111 118 119 118
## [29,] 60 61 60 70 99 113 121 121 121
## [30,] 60 60 60 82 115 132 140 140 149
## [31,] 60 60 73 109 121 162 182 182 182
## [32,] 60 67 92 121 150 182 179 182 182
## [33,] 60 82 103 121 154 182 182 182 170
## [34,] 97 100 120 143 164 178 181 182 182
## [35,] 110 113 130 153 182 179 182 182 182
## [36,] 118 118 129 149 162 182 182 182 182
## [37,] 121 121 123 129 144 156 170 182 182
## [38,] 121 121 121 121 121 136 152 156 178
## [39,] 121 121 121 121 121 121 129 130 153
## [40,] 121 121 121 121 121 121 121 121 129
## [41,] 121 121 121 121 121 121 121 121 121
## [42,] 121 121 121 121 121 121 121 121 121
## [43,] 121 121 121 121 121 121 121 121 121
## [44,] 121 121 121 121 121 121 121 121 121
## [45,] 121 121 121 121 121 121 121 121 121
## [46,] 121 121 121 121 121 121 121 121 121
## [47,] 121 121 121 121 121 121 121 121 121
## [48,] 121 121 121 121 121 121 121 121 121
## [49,] 121 121 121 121 121 121 121 121 121
## [50,] 121 121 121 121 121 121 121 121 121
## [51,] 121 121 121 121 121 121 121 121 121
## [52,] 121 121 121 121 121 121 121 121 121
## [53,] 121 121 121 121 121 121 121 121 121
## [54,] 121 121 121 121 125 126 124 122 121
## [55,] 121 121 121 133 134 135 131 124 121
## [56,] 121 121 135 145 146 148 141 127 121
## [57,] 128 139 146 160 171 182 163 140 121
## [58,] 145 148 160 170 182 179 182 153 138
## [59,] 163 168 172 182 184 184 176 170 170
## [60,] 182 178 178 182 192 196 188 182 182
## [61,] 184 185 181 191 203 214 225 203 186
## [62,] 189 196 203 208 220 231 243 215 182
## [63,] 202 213 220 227 233 240 242 222 202
## [64,] 232 231 235 238 240 241 242 233 206
## [65,] 243 243 243 243 242 242 240 243 207
## [66,] 245 243 243 243 243 243 207 182 182
## [67,] 247 244 243 240 228 192 186 189 182
## [68,] 255 243 243 231 211 182 185 183 183
## [69,] 276 265 248 243 213 195 182 180 171
## [70,] 302 292 261 243 217 185 182 175 163
## [71,] 303 304 270 243 219 193 182 182 169
## [72,] 303 294 253 242 228 218 214 206 195
## [73,] 304 304 243 243 242 241 243 243 226
## [74,] 296 275 243 243 243 267 289 269 256
## [75,] 294 278 264 243 284 304 297 304 304
## [76,] 309 297 282 291 300 303 304 284 255
## [77,] 332 317 304 301 295 275 243 243 243
## [78,] 357 342 327 311 291 259 248 244 243
## [79,] 380 365 350 333 311 283 254 244 244
## [80,] 384 372 365 347 316 292 282 263 243
## [81,] 375 371 368 366 345 318 309 294 276
## [82,] 368 367 366 366 365 349 332 313 304
## [83,] 367 366 366 365 365 365 356 326 309
## [,1061] [,1062] [,1063] [,1064] [,1065] [,1066] [,1067] [,1068] [,1069]
## [1,] 43 41 39 37 37 36 36 36 37
## [2,] 44 42 40 39 39 39 39 39 39
## [3,] 45 43 42 41 41 42 42 41 40
## [4,] 47 46 46 45 45 46 44 43 43
## [5,] 50 50 50 49 48 49 47 47 47
## [6,] 54 55 54 52 51 52 51 50 50
## [7,] 59 59 58 56 55 55 54 53 54
## [8,] 60 60 60 59 58 57 57 57 57
## [9,] 60 60 60 60 60 60 59 60 60
## [10,] 60 61 61 60 60 60 60 60 60
## [11,] 61 62 63 61 61 61 61 61 61
## [12,] 62 66 69 64 65 63 64 64 63
## [13,] 65 73 79 72 68 66 67 66 66
## [14,] 68 80 86 76 70 67 68 68 68
## [15,] 75 93 98 80 72 69 71 71 71
## [16,] 83 111 107 82 73 71 74 74 74
## [17,] 88 121 118 83 73 73 77 77 79
## [18,] 60 105 94 81 74 75 80 83 89
## [19,] 60 65 81 70 67 74 82 90 103
## [20,] 60 60 60 62 60 60 77 90 112
## [21,] 60 60 60 60 60 63 64 76 94
## [22,] 60 60 60 60 60 60 60 66 87
## [23,] 60 60 60 60 60 60 60 60 79
## [24,] 60 60 60 60 60 60 60 60 68
## [25,] 72 60 60 60 60 60 60 60 60
## [26,] 92 72 60 60 60 60 60 60 60
## [27,] 101 78 60 60 60 60 60 60 60
## [28,] 115 99 84 68 60 60 60 60 68
## [29,] 122 121 106 91 76 60 60 60 75
## [30,] 135 122 121 114 99 88 68 66 84
## [31,] 151 128 122 121 121 121 89 86 95
## [32,] 159 129 122 121 121 121 102 99 104
## [33,] 142 121 121 121 121 121 111 112 114
## [34,] 177 155 140 127 121 121 120 121 121
## [35,] 182 182 167 143 123 121 121 123 123
## [36,] 182 182 182 152 121 123 121 129 128
## [37,] 182 182 182 175 147 121 139 143 137
## [38,] 182 182 182 182 167 170 172 163 148
## [39,] 175 182 182 182 182 182 180 182 156
## [40,] 152 165 182 182 182 182 182 160 150
## [41,] 129 133 147 163 172 174 166 146 135
## [42,] 121 121 121 137 147 149 145 131 125
## [43,] 121 121 121 121 128 129 129 122 121
## [44,] 121 121 121 121 121 122 123 121 118
## [45,] 121 121 121 121 121 121 121 118 115
## [46,] 121 121 121 121 121 121 121 115 110
## [47,] 121 121 121 121 121 121 117 111 106
## [48,] 121 121 121 121 121 121 115 107 100
## [49,] 121 121 121 121 121 121 112 103 95
## [50,] 121 121 121 121 121 121 111 102 93
## [51,] 121 121 121 121 121 121 111 103 94
## [52,] 121 121 121 121 121 121 112 105 98
## [53,] 121 121 121 121 121 121 113 108 104
## [54,] 121 121 121 121 121 121 116 113 112
## [55,] 121 121 121 121 121 121 121 120 121
## [56,] 121 121 121 121 121 121 121 121 124
## [57,] 121 121 121 141 158 136 135 134 130
## [58,] 121 121 145 156 182 170 167 159 140
## [59,] 151 140 153 166 176 182 182 182 158
## [60,] 182 173 169 168 178 181 182 182 163
## [61,] 182 181 176 171 166 167 162 170 165
## [62,] 183 178 171 164 150 134 121 141 145
## [63,] 188 183 178 167 146 121 123 122 121
## [64,] 194 187 183 182 153 121 121 121 121
## [65,] 193 185 183 174 145 132 124 121 121
## [66,] 182 179 171 161 142 134 128 124 121
## [67,] 182 172 164 155 143 134 128 123 121
## [68,] 175 161 151 141 133 126 123 122 121
## [69,] 162 147 135 126 121 123 122 121 121
## [70,] 151 128 123 122 122 121 122 121 121
## [71,] 162 151 121 121 121 121 132 129 126
## [72,] 191 186 171 167 179 170 151 139 131
## [73,] 216 204 191 181 182 182 167 149 133
## [74,] 237 223 203 185 182 179 169 153 137
## [75,] 259 243 196 184 182 182 175 155 138
## [76,] 259 243 205 182 183 182 182 151 132
## [77,] 243 243 216 182 183 163 153 131 125
## [78,] 243 243 221 182 183 165 146 121 121
## [79,] 243 243 201 187 184 171 160 149 144
## [80,] 243 228 198 188 184 183 179 175 174
## [81,] 255 243 213 196 194 198 193 188 183
## [82,] 270 243 229 227 230 243 225 204 186
## [83,] 294 260 242 238 241 242 243 218 190
## [,1070] [,1071] [,1072] [,1073] [,1074] [,1075] [,1076] [,1077] [,1078]
## [1,] 37 38 38 38 38 37 37 36 36
## [2,] 39 38 38 38 38 38 38 38 38
## [3,] 40 39 39 39 39 39 39 39 39
## [4,] 42 42 42 42 42 42 42 41 41
## [5,] 46 46 45 45 45 45 44 43 43
## [6,] 49 49 48 48 48 47 47 45 45
## [7,] 53 51 50 51 51 50 49 47 47
## [8,] 56 54 53 53 53 53 51 49 48
## [9,] 59 57 56 56 56 55 53 50 50
## [10,] 60 59 59 59 59 58 55 52 51
## [11,] 61 60 60 61 60 59 57 54 53
## [12,] 62 60 62 62 61 60 59 55 53
## [13,] 65 65 64 63 62 61 59 56 55
## [14,] 68 69 67 66 64 63 61 58 57
## [15,] 72 72 71 69 67 65 62 60 58
## [16,] 76 76 75 73 71 68 62 60 60
## [17,] 83 85 83 80 78 74 66 60 60
## [18,] 97 103 96 92 88 81 71 68 65
## [19,] 116 121 110 104 100 92 78 75 73
## [20,] 121 115 115 115 113 103 85 81 79
## [21,] 106 113 117 121 121 107 92 88 83
## [22,] 94 103 111 115 119 107 98 94 89
## [23,] 87 97 107 113 118 110 103 99 95
## [24,] 78 90 102 111 118 117 110 105 101
## [25,] 69 87 103 113 121 121 117 111 107
## [26,] 60 89 116 117 119 121 121 119 116
## [27,] 82 95 121 121 121 121 121 121 121
## [28,] 86 104 117 121 121 121 121 121 121
## [29,] 93 107 114 117 120 121 121 121 121
## [30,] 99 110 115 117 118 120 121 121 121
## [31,] 104 111 114 116 118 120 121 121 121
## [32,] 107 111 113 115 118 120 121 121 121
## [33,] 113 113 114 116 118 120 121 121 121
## [34,] 118 117 117 117 119 121 121 121 121
## [35,] 121 120 120 119 120 121 121 121 121
## [36,] 124 121 121 121 121 121 121 121 121
## [37,] 130 124 121 121 121 121 121 121 121
## [38,] 135 126 123 121 121 121 121 121 121
## [39,] 137 124 121 121 121 121 121 121 121
## [40,] 134 127 122 121 121 121 121 121 121
## [41,] 127 124 122 122 121 121 121 121 121
## [42,] 123 122 122 121 121 121 121 121 121
## [43,] 121 121 121 121 121 121 121 121 121
## [44,] 117 118 121 121 121 121 121 121 121
## [45,] 114 114 117 121 121 121 121 121 121
## [46,] 108 106 107 114 121 121 121 121 121
## [47,] 101 98 96 98 102 111 121 111 121
## [48,] 94 88 82 80 80 81 80 76 72
## [49,] 87 78 68 60 60 60 60 63 60
## [50,] 84 75 63 61 60 60 60 60 60
## [51,] 87 80 70 60 60 60 60 60 60
## [52,] 93 88 78 71 68 67 66 64 62
## [53,] 101 96 86 78 75 73 71 69 66
## [54,] 111 103 92 82 79 77 74 72 69
## [55,] 121 112 99 88 86 83 79 76 72
## [56,] 122 121 107 95 92 88 85 81 75
## [57,] 125 122 110 101 98 94 90 86 80
## [58,] 130 121 111 107 104 100 96 92 85
## [59,] 140 127 117 114 110 106 102 97 91
## [60,] 151 139 121 121 117 112 107 103 96
## [61,] 160 160 169 147 127 119 113 110 102
## [62,] 158 171 182 182 141 128 121 121 110
## [63,] 132 160 170 145 137 128 123 122 119
## [64,] 121 129 142 141 133 125 121 121 121
## [65,] 121 121 128 130 128 121 121 121 121
## [66,] 121 121 121 122 122 122 121 121 121
## [67,] 121 121 121 121 121 121 121 121 121
## [68,] 121 121 121 121 121 121 121 121 121
## [69,] 121 121 121 121 121 121 121 121 121
## [70,] 122 121 121 121 121 121 121 121 121
## [71,] 122 121 121 121 121 121 121 121 121
## [72,] 123 121 121 121 121 121 121 121 121
## [73,] 122 121 121 121 121 121 121 121 121
## [74,] 125 121 121 121 121 121 121 121 121
## [75,] 124 122 121 121 124 122 122 121 120
## [76,] 122 121 121 130 126 123 122 121 120
## [77,] 122 140 154 139 129 124 122 120 119
## [78,] 152 182 182 145 128 121 122 120 119
## [79,] 172 182 165 131 124 123 122 119 118
## [80,] 175 155 142 121 122 123 122 121 121
## [81,] 169 144 121 126 123 121 134 133 130
## [82,] 166 149 135 121 121 151 172 160 148
## [83,] 172 159 145 140 153 172 196 189 174
## [,1079] [,1080] [,1081] [,1082] [,1083] [,1084] [,1085] [,1086] [,1087]
## [1,] 36 36 36 35 35 36 38 41 44
## [2,] 38 39 39 40 41 42 44 46 48
## [3,] 41 43 43 44 45 47 48 50 51
## [4,] 43 44 45 45 47 49 50 51 52
## [5,] 45 46 46 47 48 50 51 52 53
## [6,] 46 48 48 48 49 51 52 53 54
## [7,] 48 49 49 49 50 52 53 53 54
## [8,] 49 50 51 50 51 52 53 54 55
## [9,] 51 51 52 52 52 53 54 55 56
## [10,] 52 53 53 53 53 54 55 56 57
## [11,] 53 54 54 54 54 55 56 57 58
## [12,] 54 55 55 55 55 56 57 58 58
## [13,] 56 56 56 56 56 57 58 58 59
## [14,] 57 57 58 57 57 58 59 59 59
## [15,] 58 58 59 58 58 59 59 59 59
## [16,] 60 60 60 59 59 59 59 59 60
## [17,] 60 62 62 61 60 60 60 60 60
## [18,] 67 66 65 62 60 60 60 60 60
## [19,] 72 70 68 64 61 60 60 60 60
## [20,] 78 75 72 67 63 61 60 60 60
## [21,] 81 78 75 70 66 64 61 60 60
## [22,] 87 83 80 74 69 66 63 61 61
## [23,] 92 88 84 78 72 68 65 62 60
## [24,] 97 93 88 81 75 70 65 61 61
## [25,] 104 100 91 83 78 72 66 62 60
## [26,] 116 109 98 89 82 74 67 60 60
## [27,] 121 121 106 97 89 79 70 60 60
## [28,] 121 119 116 114 102 89 77 66 60
## [29,] 121 121 121 121 121 101 90 81 84
## [30,] 121 121 121 121 119 110 103 98 96
## [31,] 121 121 121 121 121 119 117 117 113
## [32,] 121 121 121 121 121 121 121 120 121
## [33,] 121 121 121 121 121 121 121 121 121
## [34,] 121 121 121 121 121 121 121 121 121
## [35,] 121 121 121 121 121 121 121 121 121
## [36,] 121 121 121 120 119 120 121 121 120
## [37,] 121 120 119 118 117 117 117 117 119
## [38,] 121 120 118 116 114 113 114 115 118
## [39,] 121 119 116 113 111 109 110 112 118
## [40,] 121 116 111 107 103 99 102 107 119
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## [59,] 84 79 74 69 65 63 61 60 60
## [60,] 88 83 78 73 67 63 60 60 60
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## [62,] 99 94 87 79 69 60 60 60 60
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## [71,] 121 121 121 121 121 121 121 121 121
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## [81,] 124 119 112 106 98 89 82 76 69
## [82,] 135 121 118 109 99 92 85 78 71
## [83,] 159 140 126 116 104 95 87 79 71
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## [75,] 121 121 121 121 106 92 79 67 61
## [76,] 121 120 121 121 105 90 76 60 61
## [77,] 110 116 121 121 101 87 74 68 61
## [78,] 96 101 121 101 95 84 74 67 62
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## [81,] 63 60 60 60 62 62 62 62 61
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## [83,] 65 61 60 60 60 60 60 60 60
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## [2,] 63 65 65 63 61 58 53 49 45
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## [4,] 62 64 64 64 63 62 60 57 54
## [5,] 60 61 61 61 61 60 60 59 58
## [6,] 60 60 60 60 60 60 60 60 60
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## [51,] 60 60 60 60 60 60 60 60 60
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## [83,] 60 60 60 60 60 60 60 60 60
## [,1106] [,1107] [,1108] [,1109] [,1110] [,1111] [,1112] [,1113] [,1114]
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## [2,] 41 39 36 34 31 27 25 23 22
## [3,] 45 42 40 37 33 29 26 25 24
## [4,] 50 47 44 41 37 31 27 25 23
## [5,] 55 52 49 45 40 33 28 24 22
## [6,] 58 55 52 48 42 34 28 24 22
## [7,] 60 58 55 50 43 35 29 24 22
## [8,] 60 59 56 50 42 34 27 23 22
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## [11,] 60 60 57 50 42 33 26 21 21
## [12,] 60 60 59 51 42 33 24 21 22
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## [19,] 60 60 57 50 42 34 25 23 25
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## [22,] 60 60 60 51 43 34 26 18 25
## [23,] 60 60 60 52 43 35 26 18 28
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## [29,] 60 60 60 53 45 37 28 20 30
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## [34,] 60 60 60 58 47 39 29 26 34
## [35,] 60 60 60 60 47 39 30 27 34
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## [44,] 60 60 60 55 53 42 29 35 38
## [45,] 60 60 60 56 54 42 29 35 38
## [46,] 60 60 60 57 55 42 30 36 39
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## [48,] 60 60 60 59 58 42 30 37 39
## [49,] 60 60 60 60 59 41 31 37 40
## [50,] 60 60 60 60 60 41 31 38 40
## [51,] 60 60 60 60 49 40 31 38 40
## [52,] 60 60 60 60 49 40 32 39 41
## [53,] 60 60 60 60 49 38 32 39 41
## [54,] 60 60 60 60 49 37 31 39 42
## [55,] 60 60 60 60 50 38 32 40 42
## [56,] 60 60 60 60 50 38 32 40 42
## [57,] 60 60 60 60 50 39 33 41 43
## [58,] 60 60 60 60 50 37 33 41 43
## [59,] 60 60 60 60 50 39 34 42 43
## [60,] 60 60 60 60 50 39 34 42 44
## [61,] 60 60 60 60 50 39 35 42 44
## [62,] 60 60 60 60 50 40 35 43 44
## [63,] 60 60 60 60 50 40 36 43 45
## [64,] 60 60 60 60 46 38 37 44 45
## [65,] 60 60 60 60 47 39 37 44 46
## [66,] 60 60 60 60 47 39 38 45 46
## [67,] 60 60 60 60 47 40 38 45 46
## [68,] 60 60 60 60 47 40 39 46 47
## [69,] 60 60 60 60 47 41 39 46 47
## [70,] 60 60 60 60 48 41 40 46 47
## [71,] 60 60 60 60 48 42 40 47 48
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## [75,] 60 60 60 56 46 44 43 48 49
## [76,] 60 60 60 56 47 44 43 49 49
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## [80,] 60 60 60 56 48 46 46 50 51
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## [83,] 60 60 60 56 50 48 47 52 52
## [,1115] [,1116] [,1117] [,1118] [,1119] [,1120] [,1121] [,1122] [,1123]
## [1,] 18 17 17 17 17 18 19 20 21
## [2,] 21 21 21 21 22 23 24 26 28
## [3,] 24 24 24 25 26 27 29 31 33
## [4,] 23 24 25 25 26 28 30 33 35
## [5,] 22 24 25 25 26 29 31 34 36
## [6,] 22 24 25 26 27 29 31 34 37
## [7,] 22 25 26 26 27 29 31 35 37
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## [11,] 23 26 27 27 28 31 33 37 38
## [12,] 25 27 28 28 29 31 33 37 39
## [13,] 26 28 28 28 29 31 33 37 39
## [14,] 27 28 28 28 29 32 34 37 39
## [15,] 27 28 29 29 30 32 34 38 39
## [16,] 27 29 29 29 30 32 34 38 39
## [17,] 28 29 29 29 30 32 34 38 40
## [18,] 28 30 30 30 31 33 35 39 40
## [19,] 28 30 30 30 31 33 36 39 40
## [20,] 29 30 30 30 31 33 37 40 40
## [21,] 29 31 31 31 31 34 37 40 41
## [22,] 30 31 31 31 31 34 37 40 41
## [23,] 31 32 32 32 32 35 37 41 41
## [24,] 31 32 32 32 32 35 38 41 41
## [25,] 32 32 32 32 32 35 38 41 41
## [26,] 32 32 32 32 32 35 38 41 42
## [27,] 32 33 33 33 33 36 39 41 42
## [28,] 33 33 33 33 33 36 39 42 42
## [29,] 33 33 33 33 33 37 40 42 42
## [30,] 33 34 34 34 34 37 41 42 42
## [31,] 34 34 34 34 34 37 41 42 43
## [32,] 34 35 35 35 34 38 42 42 43
## [33,] 35 35 35 35 35 38 42 43 43
## [34,] 35 35 35 35 35 38 42 43 43
## [35,] 35 35 35 35 35 39 42 43 43
## [36,] 36 36 36 36 36 39 42 43 44
## [37,] 36 36 36 36 36 39 43 44 44
## [38,] 36 37 37 36 36 40 43 44 44
## [39,] 37 37 37 37 38 40 43 44 44
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## [42,] 38 38 38 38 39 41 44 45 45
## [43,] 38 38 38 38 39 42 44 45 45
## [44,] 39 39 39 38 40 42 44 45 46
## [45,] 39 39 39 39 40 42 45 46 46
## [46,] 39 39 39 39 40 42 45 46 46
## [47,] 39 40 39 39 40 42 45 46 46
## [48,] 40 40 40 40 41 43 45 46 46
## [49,] 40 40 40 40 41 43 46 46 46
## [50,] 41 41 40 40 43 43 46 46 47
## [51,] 41 41 41 41 43 44 46 47 47
## [52,] 41 41 41 41 43 44 46 47 47
## [53,] 42 42 42 41 44 44 47 47 47
## [54,] 42 42 42 42 44 45 47 47 48
## [55,] 42 42 42 42 44 45 47 48 48
## [56,] 43 43 42 42 45 45 47 48 48
## [57,] 43 43 43 43 45 45 47 48 48
## [58,] 43 43 43 43 45 46 48 48 48
## [59,] 44 44 43 43 45 46 48 49 49
## [60,] 44 44 44 44 46 46 48 49 49
## [61,] 44 44 44 44 46 46 49 49 49
## [62,] 45 45 44 44 46 47 49 49 49
## [63,] 45 45 45 45 46 47 49 49 49
## [64,] 45 45 45 45 47 47 49 49 50
## [65,] 46 46 46 45 47 47 49 50 50
## [66,] 46 46 46 46 48 48 49 50 50
## [67,] 46 46 46 46 48 48 50 50 50
## [68,] 47 47 46 46 48 48 50 50 50
## [69,] 47 47 47 47 48 49 50 51 51
## [70,] 47 47 47 47 49 49 50 51 51
## [71,] 48 48 47 47 49 49 51 51 51
## [72,] 48 48 48 48 49 49 51 51 51
## [73,] 48 48 48 48 49 50 51 51 51
## [74,] 49 49 48 48 50 50 51 52 52
## [75,] 49 49 49 49 50 50 52 52 52
## [76,] 49 49 49 49 50 50 52 52 52
## [77,] 50 50 49 49 50 51 52 52 52
## [78,] 50 50 50 49 51 51 52 52 52
## [79,] 50 50 50 50 51 51 53 53 53
## [80,] 51 51 50 50 51 51 53 53 53
## [81,] 51 51 51 50 52 52 53 53 53
## [82,] 51 51 51 51 52 52 53 53 53
## [83,] 52 52 51 51 52 52 53 53 53
## [,1124] [,1125] [,1126] [,1127] [,1128] [,1129] [,1130] [,1131] [,1132]
## [1,] 22 23 24 25 26 27 28 29 29
## [2,] 29 30 31 33 34 36 37 38 38
## [3,] 34 36 37 39 41 43 44 45 45
## [4,] 37 38 40 42 44 46 48 49 49
## [5,] 37 38 41 42 44 47 49 50 50
## [6,] 38 39 41 42 44 48 49 50 50
## [7,] 38 39 41 43 45 48 50 50 50
## [8,] 38 39 41 43 45 48 50 50 50
## [9,] 38 39 42 43 45 48 50 50 50
## [10,] 39 39 42 43 45 48 50 50 50
## [11,] 39 39 42 44 45 48 50 50 50
## [12,] 39 39 42 44 44 49 50 50 50
## [13,] 39 39 42 44 45 49 50 50 51
## [14,] 39 39 42 44 45 49 50 51 51
## [15,] 39 39 43 44 47 50 50 51 51
## [16,] 40 40 43 44 47 50 51 51 51
## [17,] 40 40 43 45 47 50 51 51 51
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## [19,] 40 40 43 45 47 50 51 51 51
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## [21,] 41 41 44 45 48 50 51 51 51
## [22,] 41 41 44 46 47 50 51 51 51
## [23,] 41 41 44 46 48 51 51 51 51
## [24,] 41 41 44 46 48 51 51 51 51
## [25,] 42 42 45 46 48 51 51 51 52
## [26,] 42 42 45 46 50 51 51 52 52
## [27,] 42 42 45 47 50 51 52 52 52
## [28,] 42 42 45 47 50 51 52 52 52
## [29,] 42 42 45 47 50 51 52 52 52
## [30,] 43 43 46 47 50 51 52 52 52
## [31,] 43 43 46 47 50 51 52 52 52
## [32,] 43 43 46 47 50 52 52 52 52
## [33,] 43 43 46 48 50 52 52 52 52
## [34,] 43 43 46 48 51 52 52 52 52
## [35,] 44 44 47 48 51 52 52 52 52
## [36,] 44 44 47 48 51 52 52 52 52
## [37,] 44 44 47 48 51 52 52 52 53
## [38,] 44 44 48 48 51 52 52 53 53
## [39,] 45 45 48 49 51 52 53 53 53
## [40,] 45 45 48 49 51 52 53 53 52
## [41,] 45 45 48 49 52 53 53 53 51
## [42,] 45 45 48 49 52 53 53 53 51
## [43,] 45 45 48 49 52 53 53 53 52
## [44,] 46 46 48 49 52 53 53 53 52
## [45,] 46 47 49 49 52 53 53 53 52
## [46,] 46 47 49 49 52 53 53 53 52
## [47,] 46 47 49 49 52 53 53 53 52
## [48,] 46 48 49 50 52 53 53 53 52
## [49,] 46 48 50 50 52 53 53 53 52
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## [51,] 47 48 50 50 53 53 53 53 51
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## [53,] 47 49 50 50 53 53 53 54 51
## [54,] 48 49 50 51 53 53 54 54 51
## [55,] 48 50 51 51 53 54 54 54 52
## [56,] 48 50 51 51 53 54 54 54 52
## [57,] 48 50 51 51 53 54 54 54 52
## [58,] 48 51 51 51 53 54 54 54 52
## [59,] 49 51 51 51 53 54 54 54 52
## [60,] 49 51 51 51 53 54 54 54 52
## [61,] 49 51 52 52 54 54 54 54 52
## [62,] 49 51 52 52 54 54 54 54 52
## [63,] 49 51 52 52 54 54 54 54 53
## [64,] 50 52 52 52 54 54 54 54 53
## [65,] 50 52 52 52 54 54 54 54 53
## [66,] 50 52 52 52 54 54 55 55 53
## [67,] 50 52 52 52 54 55 55 55 53
## [68,] 50 52 53 53 54 55 55 55 53
## [69,] 51 52 53 53 54 55 55 55 53
## [70,] 51 53 53 53 55 55 55 55 53
## [71,] 51 53 53 53 55 55 55 55 53
## [72,] 51 53 53 53 55 55 55 55 53
## [73,] 51 53 53 53 55 55 55 55 54
## [74,] 52 53 53 53 55 55 55 55 54
## [75,] 52 53 53 53 55 55 55 55 54
## [76,] 52 53 54 54 55 55 55 55 54
## [77,] 52 53 54 54 55 55 55 55 54
## [78,] 52 54 54 54 55 55 55 55 54
## [79,] 53 54 54 54 55 56 56 56 54
## [80,] 53 54 54 54 56 56 56 56 55
## [81,] 53 54 54 54 56 56 56 56 55
## [82,] 53 54 55 55 56 56 56 56 55
## [83,] 53 55 55 55 56 56 56 56 55
## [,1133] [,1134] [,1135] [,1136] [,1137] [,1138] [,1139] [,1140] [,1141]
## [1,] 29 29 30 30 30 31 32 33 33
## [2,] 38 38 38 38 39 40 41 42 42
## [3,] 45 45 45 45 46 47 48 49 49
## [4,] 48 48 49 49 49 50 52 53 54
## [5,] 48 49 49 50 50 51 53 55 56
## [6,] 48 49 49 50 50 51 53 55 56
## [7,] 48 49 49 50 50 51 53 55 56
## [8,] 48 49 49 50 50 51 53 55 56
## [9,] 48 49 50 50 50 51 54 55 56
## [10,] 48 49 50 50 50 51 54 55 56
## [11,] 48 49 50 50 50 51 54 55 56
## [12,] 47 49 50 50 51 51 54 55 56
## [13,] 47 49 50 51 51 51 54 55 56
## [14,] 48 49 50 51 51 51 54 55 56
## [15,] 48 49 50 51 51 51 54 56 56
## [16,] 48 49 51 51 51 51 54 56 56
## [17,] 48 49 51 51 51 51 54 56 56
## [18,] 48 50 51 51 51 51 54 56 56
## [19,] 48 50 51 51 51 51 54 56 56
## [20,] 48 50 51 51 51 51 54 56 56
## [21,] 48 50 51 51 51 51 54 56 56
## [22,] 48 50 51 51 51 51 54 56 56
## [23,] 48 51 51 51 51 51 55 56 56
## [24,] 49 51 51 51 52 52 55 56 56
## [25,] 49 51 51 52 52 52 55 56 56
## [26,] 49 51 52 52 52 52 55 56 56
## [27,] 49 51 52 52 52 52 55 56 57
## [28,] 49 51 52 52 52 52 55 56 57
## [29,] 49 51 52 52 52 52 55 56 57
## [30,] 49 51 52 52 52 52 55 56 57
## [31,] 50 52 52 52 52 52 55 56 57
## [32,] 50 52 52 52 52 52 55 56 57
## [33,] 50 52 52 52 52 52 55 56 57
## [34,] 50 52 52 52 52 52 55 56 57
## [35,] 50 52 52 52 52 53 55 56 57
## [36,] 50 52 52 53 53 53 56 57 57
## [37,] 51 52 53 53 53 53 56 57 57
## [38,] 51 52 53 53 53 53 56 57 57
## [39,] 51 53 53 53 53 53 56 57 57
## [40,] 51 53 53 53 53 53 56 57 57
## [41,] 52 53 53 53 53 53 56 57 57
## [42,] 52 53 53 53 53 53 56 57 57
## [43,] 52 53 53 53 53 53 56 57 57
## [44,] 52 53 53 53 53 53 56 57 57
## [45,] 52 53 53 53 53 53 56 57 57
## [46,] 53 53 53 53 53 53 56 57 57
## [47,] 53 53 53 53 53 55 57 57 57
## [48,] 53 53 53 53 53 55 57 57 57
## [49,] 53 53 53 53 53 55 57 57 57
## [50,] 53 53 53 53 53 55 57 57 57
## [51,] 53 53 53 54 54 55 57 57 57
## [52,] 53 53 54 54 54 55 57 57 57
## [53,] 53 54 54 54 54 55 57 57 57
## [54,] 53 54 54 54 54 55 57 57 57
## [55,] 53 54 54 54 54 55 57 57 57
## [56,] 53 54 54 54 54 55 57 57 57
## [57,] 53 54 54 54 54 56 57 57 57
## [58,] 54 54 54 54 54 56 57 57 57
## [59,] 54 54 54 54 54 56 57 57 57
## [60,] 54 54 54 54 54 56 57 57 57
## [61,] 54 54 54 54 54 56 57 57 57
## [62,] 54 54 54 54 54 56 57 57 57
## [63,] 54 54 54 55 55 56 57 57 57
## [64,] 54 55 55 55 55 56 57 57 57
## [65,] 54 55 55 55 55 56 57 57 58
## [66,] 54 55 55 55 55 56 57 57 58
## [67,] 54 55 55 55 55 57 57 57 58
## [68,] 55 55 55 55 55 57 57 57 58
## [69,] 55 55 55 55 55 57 57 57 58
## [70,] 55 55 55 55 55 57 57 57 58
## [71,] 55 55 55 55 55 57 57 57 58
## [72,] 55 55 55 55 55 57 57 57 58
## [73,] 55 55 55 55 55 57 57 57 58
## [74,] 55 55 55 55 55 57 57 57 58
## [75,] 55 55 56 56 56 57 57 58 58
## [76,] 55 56 56 56 56 57 57 58 58
## [77,] 55 56 56 56 56 57 57 58 58
## [78,] 56 56 56 56 56 57 57 58 58
## [79,] 56 56 56 56 56 57 57 58 58
## [80,] 56 56 56 56 56 57 57 58 58
## [81,] 56 56 56 56 56 57 57 58 58
## [82,] 56 56 56 56 56 57 57 58 58
## [83,] 56 56 56 56 56 57 57 58 58
## [,1142] [,1143] [,1144] [,1145] [,1146] [,1147] [,1148] [,1149] [,1150]
## [1,] 33 33 33 33 33 34 34 34 33
## [2,] 42 42 42 42 42 43 42 42 41
## [3,] 49 49 49 49 49 50 49 48 47
## [4,] 54 54 54 54 54 54 52 51 50
## [5,] 56 56 56 56 56 55 53 51 51
## [6,] 56 56 56 56 56 56 53 51 51
## [7,] 56 56 56 56 56 56 53 52 51
## [8,] 56 56 56 56 56 56 53 52 51
## [9,] 56 56 56 56 56 56 53 52 51
## [10,] 56 56 56 56 56 56 53 52 51
## [11,] 56 56 56 56 56 56 53 52 51
## [12,] 56 56 56 56 56 56 53 52 52
## [13,] 56 56 56 56 56 56 53 52 52
## [14,] 56 56 56 56 56 57 53 52 52
## [15,] 56 56 56 56 57 57 53 52 52
## [16,] 56 56 56 57 57 57 53 52 52
## [17,] 56 56 57 57 57 57 53 53 53
## [18,] 56 57 57 57 57 57 54 53 53
## [19,] 56 57 57 57 57 57 54 53 53
## [20,] 56 57 57 57 57 57 54 53 53
## [21,] 57 57 57 57 57 57 54 53 53
## [22,] 57 57 57 57 57 57 54 53 53
## [23,] 57 57 57 57 57 56 54 53 53
## [24,] 57 57 57 57 57 56 54 54 54
## [25,] 57 57 57 57 57 56 54 54 54
## [26,] 57 57 57 57 57 56 54 54 54
## [27,] 57 57 57 57 57 56 54 54 54
## [28,] 57 57 57 57 57 56 55 54 54
## [29,] 57 57 57 57 57 56 55 54 54
## [30,] 57 57 57 57 57 56 55 55 55
## [31,] 57 57 57 57 57 56 55 55 55
## [32,] 57 57 57 57 57 56 55 55 55
## [33,] 57 57 57 57 57 56 55 55 55
## [34,] 57 57 57 57 57 56 55 55 55
## [35,] 57 57 57 57 57 56 56 56 56
## [36,] 57 57 57 57 57 56 56 56 56
## [37,] 57 57 57 57 57 56 56 56 56
## [38,] 57 57 57 57 57 56 56 56 56
## [39,] 57 57 57 57 57 56 56 56 56
## [40,] 57 57 57 57 57 57 56 56 56
## [41,] 57 57 57 57 57 57 57 57 57
## [42,] 57 57 57 57 57 57 57 57 57
## [43,] 57 57 57 57 57 57 57 57 57
## [44,] 57 57 57 58 57 57 57 57 57
## [45,] 57 57 57 58 58 58 58 58 58
## [46,] 57 57 57 58 58 58 58 58 58
## [47,] 57 57 58 58 58 58 58 58 58
## [48,] 57 57 58 58 58 58 58 58 58
## [49,] 57 57 58 58 58 58 58 58 58
## [50,] 57 57 58 58 58 58 58 58 58
## [51,] 57 57 58 58 58 58 58 58 58
## [52,] 57 57 58 58 58 58 58 58 58
## [53,] 57 58 58 58 58 58 58 58 58
## [54,] 57 58 58 58 58 58 58 58 58
## [55,] 57 58 58 58 58 58 58 58 58
## [56,] 57 58 58 58 58 58 58 58 59
## [57,] 57 58 58 58 58 58 58 58 59
## [58,] 58 58 58 58 58 58 58 59 59
## [59,] 58 58 58 58 58 58 58 59 59
## [60,] 58 58 58 58 58 58 59 59 59
## [61,] 58 58 58 58 58 58 59 59 59
## [62,] 58 58 58 58 58 58 59 59 59
## [63,] 58 58 58 58 58 59 59 59 59
## [64,] 58 58 58 58 58 59 59 59 59
## [65,] 58 58 58 58 58 59 59 59 59
## [66,] 58 58 58 58 59 59 59 59 59
## [67,] 58 58 58 58 59 59 59 59 59
## [68,] 58 58 58 59 59 59 59 59 59
## [69,] 58 58 58 59 59 59 59 59 59
## [70,] 58 58 59 59 59 59 59 59 59
## [71,] 58 58 59 59 59 59 59 59 59
## [72,] 58 58 59 59 59 59 59 59 59
## [73,] 58 58 59 59 59 59 59 59 59
## [74,] 58 58 59 59 59 59 59 59 59
## [75,] 58 58 59 59 59 59 59 59 59
## [76,] 58 59 59 59 59 59 59 59 59
## [77,] 58 59 59 59 59 59 59 59 59
## [78,] 58 59 59 59 59 59 59 59 59
## [79,] 58 59 59 59 59 59 59 59 60
## [80,] 58 59 59 59 59 59 59 59 60
## [81,] 58 59 59 59 59 59 59 60 60
## [82,] 58 59 59 59 59 59 59 60 60
## [83,] 59 59 59 59 59 59 59 60 60
## [,1151] [,1152] [,1153] [,1154] [,1155] [,1156] [,1157] [,1158] [,1159]
## [1,] 33 33 34 34 35 35 35 35 35
## [2,] 41 41 41 41 42 42 42 42 42
## [3,] 47 47 47 47 47 47 47 47 46
## [4,] 50 50 50 50 50 50 50 49 48
## [5,] 50 50 50 50 50 50 50 50 47
## [6,] 51 51 50 50 50 50 50 50 47
## [7,] 51 51 51 51 51 51 51 51 48
## [8,] 51 51 51 51 51 51 51 51 48
## [9,] 51 51 51 51 51 51 51 51 48
## [10,] 51 51 51 51 51 51 51 51 48
## [11,] 51 51 51 51 51 51 51 51 48
## [12,] 52 52 52 52 52 52 52 52 49
## [13,] 52 52 52 52 52 52 52 52 49
## [14,] 52 52 52 52 52 52 52 52 49
## [15,] 52 52 52 52 52 52 52 52 49
## [16,] 52 52 52 52 52 52 52 52 49
## [17,] 53 53 53 53 53 53 53 53 50
## [18,] 53 53 53 53 53 53 53 53 50
## [19,] 53 53 53 53 53 53 53 53 50
## [20,] 53 53 53 53 53 53 53 53 50
## [21,] 53 53 53 53 53 53 53 53 51
## [22,] 53 53 53 53 53 53 53 53 51
## [23,] 53 53 53 53 53 53 54 54 51
## [24,] 54 54 54 54 54 54 54 54 51
## [25,] 54 54 54 54 54 54 54 54 52
## [26,] 54 54 54 54 54 54 54 54 52
## [27,] 54 54 54 54 54 54 54 54 52
## [28,] 54 54 54 54 54 54 55 55 52
## [29,] 54 54 54 54 54 55 55 55 53
## [30,] 55 55 55 55 55 55 55 55 53
## [31,] 55 55 55 55 55 55 55 55 53
## [32,] 55 55 55 55 55 55 55 55 54
## [33,] 55 55 55 55 55 55 55 55 54
## [34,] 55 55 55 55 55 56 56 56 54
## [35,] 56 56 56 56 56 56 56 56 55
## [36,] 56 56 56 56 56 56 56 56 55
## [37,] 56 56 56 56 56 56 56 56 55
## [38,] 56 56 56 56 56 56 56 56 55
## [39,] 56 56 56 56 56 56 56 56 56
## [40,] 56 56 56 56 56 57 57 57 56
## [41,] 57 57 57 57 57 57 57 57 56
## [42,] 57 57 57 57 57 57 57 57 57
## [43,] 57 57 57 57 57 57 57 57 57
## [44,] 57 57 57 57 57 57 57 57 57
## [45,] 58 58 58 58 58 58 58 58 58
## [46,] 58 58 58 58 58 58 58 58 58
## [47,] 58 58 58 58 58 58 58 59 59
## [48,] 58 58 58 58 58 58 59 59 59
## [49,] 58 58 58 58 58 58 58 58 59
## [50,] 58 58 58 58 58 58 58 58 58
## [51,] 58 58 58 58 58 58 58 58 58
## [52,] 58 58 58 58 58 58 58 58 58
## [53,] 58 59 59 59 59 59 59 59 59
## [54,] 59 59 59 59 59 59 59 59 59
## [55,] 59 59 59 59 59 59 59 59 59
## [56,] 59 59 59 59 59 59 59 59 59
## [57,] 59 59 59 59 59 59 59 59 59
## [58,] 59 59 59 59 59 59 59 59 59
## [59,] 59 59 59 59 59 59 59 59 59
## [60,] 59 59 59 59 59 59 59 59 59
## [61,] 59 59 59 59 59 59 59 59 59
## [62,] 59 59 59 59 59 59 59 59 59
## [63,] 59 59 59 59 59 59 59 59 59
## [64,] 59 59 59 59 59 59 59 59 59
## [65,] 59 59 59 59 59 59 59 59 59
## [66,] 59 59 59 59 59 59 59 59 60
## [67,] 59 59 59 59 59 59 59 60 60
## [68,] 59 59 59 59 59 59 60 60 60
## [69,] 59 59 59 59 59 59 60 60 60
## [70,] 59 59 59 59 59 60 60 60 60
## [71,] 59 59 59 59 59 60 60 60 60
## [72,] 59 59 59 59 60 60 60 60 60
## [73,] 59 59 59 60 60 60 60 60 60
## [74,] 59 59 59 60 60 60 60 60 60
## [75,] 59 59 60 60 60 60 60 60 60
## [76,] 59 60 60 60 60 60 60 60 60
## [77,] 60 60 60 60 60 60 60 60 60
## [78,] 60 60 60 60 60 60 60 60 60
## [79,] 60 60 60 60 60 60 60 60 60
## [80,] 60 60 60 60 60 60 60 60 60
## [81,] 60 60 60 60 60 60 60 60 60
## [82,] 60 60 60 60 60 60 60 60 60
## [83,] 60 60 60 60 60 60 60 60 60
## [,1160] [,1161] [,1162] [,1163] [,1164] [,1165] [,1166] [,1167] [,1168]
## [1,] 34 34 33 32 32 32 32 33 33
## [2,] 41 39 38 37 36 35 35 35 37
## [3,] 45 43 42 40 38 38 38 38 40
## [4,] 46 45 43 41 39 39 38 39 41
## [5,] 46 45 43 40 39 39 39 40 42
## [6,] 46 45 43 40 39 39 39 40 42
## [7,] 46 45 44 41 40 39 39 40 42
## [8,] 46 46 44 41 40 40 40 41 43
## [9,] 46 46 44 42 41 41 40 41 44
## [10,] 47 46 44 42 41 41 41 42 45
## [11,] 47 46 45 43 42 42 42 42 45
## [12,] 47 47 45 43 42 42 42 42 46
## [13,] 48 47 46 43 42 42 42 42 46
## [14,] 48 47 45 44 43 43 43 43 47
## [15,] 48 48 45 44 43 43 43 43 47
## [16,] 48 48 45 44 44 44 44 44 47
## [17,] 49 48 46 44 44 44 44 44 48
## [18,] 49 49 46 45 45 45 45 45 48
## [19,] 49 49 46 45 45 45 45 45 49
## [20,] 49 49 47 46 46 46 46 47 49
## [21,] 50 50 47 46 46 46 46 48 50
## [22,] 50 50 48 47 47 47 47 48 50
## [23,] 51 50 48 47 47 47 47 49 51
## [24,] 51 51 48 48 48 48 48 49 51
## [25,] 51 51 49 48 48 48 48 49 51
## [26,] 51 51 49 49 49 49 49 50 52
## [27,] 52 52 49 49 49 49 49 50 52
## [28,] 52 52 50 50 49 49 50 51 53
## [29,] 52 52 50 50 50 50 50 51 53
## [30,] 53 53 51 51 51 51 51 53 53
## [31,] 53 53 51 51 51 51 51 53 54
## [32,] 53 53 52 51 51 51 52 54 54
## [33,] 54 54 52 52 52 52 52 54 54
## [34,] 54 54 53 52 52 52 53 55 55
## [35,] 54 54 53 53 53 53 53 55 55
## [36,] 55 55 54 53 53 53 54 55 56
## [37,] 55 55 54 54 54 54 54 55 56
## [38,] 55 55 54 54 54 54 55 56 56
## [39,] 56 56 55 55 55 55 55 56 57
## [40,] 56 56 55 55 55 55 56 57 57
## [41,] 56 56 56 56 56 56 56 57 57
## [42,] 56 56 56 56 56 56 57 57 58
## [43,] 57 57 57 57 57 57 57 58 58
## [44,] 57 57 57 57 57 57 58 58 59
## [45,] 58 58 58 58 58 58 58 59 59
## [46,] 58 59 59 59 59 59 59 59 59
## [47,] 59 59 59 59 59 59 59 59 59
## [48,] 59 59 59 59 59 59 59 59 59
## [49,] 59 59 59 59 59 59 59 59 59
## [50,] 58 58 58 59 59 59 59 59 59
## [51,] 58 58 58 59 59 59 59 59 59
## [52,] 58 58 58 58 59 59 59 59 59
## [53,] 59 59 59 59 59 59 59 59 59
## [54,] 59 59 59 59 59 59 59 59 59
## [55,] 59 59 59 59 59 59 59 59 59
## [56,] 59 59 59 59 59 59 59 59 59
## [57,] 59 59 59 59 59 59 59 59 59
## [58,] 59 59 59 59 59 59 59 59 59
## [59,] 59 59 59 59 59 59 59 59 59
## [60,] 59 59 59 59 59 59 59 59 60
## [61,] 59 59 59 59 59 59 60 60 60
## [62,] 59 59 59 60 60 60 60 60 60
## [63,] 59 59 60 60 60 60 60 60 60
## [64,] 60 60 60 60 60 60 60 60 60
## [65,] 60 60 60 60 60 60 60 60 60
## [66,] 60 60 60 60 60 60 60 60 60
## [67,] 60 60 60 60 60 60 60 60 60
## [68,] 60 60 60 60 60 60 60 60 60
## [69,] 60 60 60 60 60 60 60 60 60
## [70,] 60 60 60 60 60 60 60 60 60
## [71,] 60 60 60 60 60 60 60 60 60
## [72,] 60 60 60 60 60 60 60 60 60
## [73,] 60 60 60 60 60 60 60 60 60
## [74,] 60 60 60 60 60 60 60 60 60
## [75,] 60 60 60 60 60 60 60 60 60
## [76,] 60 60 60 60 60 60 60 60 60
## [77,] 60 60 60 60 60 60 60 60 60
## [78,] 60 60 60 60 60 60 60 60 60
## [79,] 60 60 60 60 60 60 60 60 60
## [80,] 60 60 60 60 60 60 60 60 60
## [81,] 60 60 60 60 60 60 60 60 60
## [82,] 60 60 60 60 60 60 60 60 60
## [83,] 60 60 60 60 60 60 60 60 60
## [,1169] [,1170] [,1171] [,1172] [,1173] [,1174] [,1175] [,1176] [,1177]
## [1,] 34 35 35 34 34 34 34 34 35
## [2,] 38 39 39 38 37 36 36 36 37
## [3,] 41 42 41 40 38 38 38 38 38
## [4,] 43 43 41 40 39 38 38 38 38
## [5,] 44 44 41 40 39 39 39 39 39
## [6,] 44 44 42 40 40 39 39 39 39
## [7,] 44 44 42 41 40 40 40 39 39
## [8,] 45 45 43 41 40 40 40 40 40
## [9,] 45 45 43 42 41 41 41 40 40
## [10,] 46 46 43 42 42 41 41 41 40
## [11,] 46 46 44 42 42 42 42 41 41
## [12,] 47 47 44 43 43 43 42 42 41
## [13,] 47 47 45 43 43 43 43 42 42
## [14,] 48 48 45 44 44 43 43 42 42
## [15,] 48 48 45 44 44 44 43 43 42
## [16,] 48 49 46 45 45 44 44 43 43
## [17,] 49 49 46 45 45 45 44 44 43
## [18,] 49 49 47 46 46 46 45 44 43
## [19,] 49 50 47 46 46 46 45 45 44
## [20,] 50 50 48 47 47 46 46 45 44
## [21,] 50 51 48 48 47 47 46 46 45
## [22,] 51 51 49 48 48 48 47 46 46
## [23,] 51 51 49 48 48 48 47 47 46
## [24,] 51 52 49 49 49 49 48 47 46
## [25,] 52 52 50 49 49 49 48 47 47
## [26,] 52 52 50 50 50 49 49 48 48
## [27,] 53 53 51 50 51 50 49 49 48
## [28,] 53 53 51 51 51 51 50 49 49
## [29,] 53 53 52 52 52 51 50 50 49
## [30,] 54 54 52 52 52 52 51 51 50
## [31,] 54 54 53 53 53 52 52 51 50
## [32,] 54 55 53 53 53 53 52 51 51
## [33,] 55 55 54 54 54 53 53 52 51
## [34,] 55 55 54 55 55 54 53 53 52
## [35,] 56 56 55 55 55 54 54 53 52
## [36,] 56 56 55 55 56 55 54 53 53
## [37,] 56 56 56 56 56 55 55 54 53
## [38,] 56 57 56 56 56 56 55 54 53
## [39,] 57 57 57 57 57 56 56 55 54
## [40,] 57 57 57 58 58 57 56 56 55
## [41,] 58 58 58 58 58 58 57 56 56
## [42,] 58 58 58 59 59 58 58 57 56
## [43,] 58 59 59 59 59 59 58 58 57
## [44,] 59 59 59 60 60 60 59 58 58
## [45,] 59 60 60 60 60 60 60 59 58
## [46,] 60 60 60 60 60 60 60 60 60
## [47,] 60 60 60 60 60 60 60 60 60
## [48,] 59 60 60 60 60 60 60 60 60
## [49,] 59 59 60 60 60 60 60 60 60
## [50,] 59 59 59 60 60 60 60 60 60
## [51,] 59 59 59 60 60 60 60 60 60
## [52,] 59 59 59 59 60 60 60 60 60
## [53,] 59 59 59 59 60 60 60 60 60
## [54,] 59 59 59 59 60 60 60 60 60
## [55,] 59 59 59 60 60 60 60 60 60
## [56,] 59 59 59 59 60 60 60 60 60
## [57,] 59 59 59 59 59 59 59 60 60
## [58,] 59 59 59 59 59 59 59 59 60
## [59,] 59 59 59 59 59 59 59 59 60
## [60,] 60 60 60 60 60 60 60 60 60
## [61,] 60 60 60 60 60 60 60 60 60
## [62,] 60 60 60 60 60 60 60 60 60
## [63,] 60 60 60 60 60 60 60 60 60
## [64,] 60 60 60 60 60 60 60 60 60
## [65,] 60 60 60 60 60 60 60 60 60
## [66,] 60 60 60 60 60 60 60 60 60
## [67,] 60 60 60 60 60 60 60 60 60
## [68,] 60 60 60 60 60 60 60 60 60
## [69,] 60 60 60 60 60 60 60 60 60
## [70,] 60 60 60 60 60 60 60 60 60
## [71,] 60 60 60 60 60 60 60 60 60
## [72,] 60 60 60 60 60 60 60 60 60
## [73,] 60 60 60 60 60 60 60 60 60
## [74,] 60 60 60 60 60 60 60 60 60
## [75,] 60 60 60 60 60 60 60 60 60
## [76,] 60 60 60 60 60 60 60 60 60
## [77,] 60 60 60 60 60 60 60 60 60
## [78,] 60 60 60 60 60 60 60 60 60
## [79,] 60 60 60 60 60 60 60 60 60
## [80,] 60 60 60 60 60 60 60 60 60
## [81,] 60 60 60 60 60 60 60 60 60
## [82,] 60 60 60 60 60 60 60 60 60
## [83,] 60 60 60 60 60 60 60 60 60
## [,1178] [,1179] [,1180] [,1181] [,1182] [,1183] [,1184] [,1185] [,1186]
## [1,] 36 38 39 40 40 39 38 38 37
## [2,] 38 38 38 38 38 37 36 35 34
## [3,] 38 38 37 37 37 35 34 33 32
## [4,] 38 38 38 38 37 35 33 32 32
## [5,] 38 38 38 38 38 35 33 32 32
## [6,] 39 38 38 38 38 35 33 33 32
## [7,] 39 39 39 38 38 35 34 33 32
## [8,] 39 39 39 38 38 35 34 33 33
## [9,] 40 39 39 39 38 35 34 33 33
## [10,] 40 40 39 39 38 35 34 34 33
## [11,] 40 40 39 39 38 36 35 34 33
## [12,] 41 40 40 39 38 36 35 34 33
## [13,] 41 40 40 39 38 36 35 34 33
## [14,] 41 41 40 39 38 36 35 35 34
## [15,] 42 41 40 39 38 37 36 35 34
## [16,] 42 41 40 39 38 37 36 35 35
## [17,] 42 41 41 39 38 37 37 36 35
## [18,] 42 42 41 40 39 38 37 36 35
## [19,] 43 42 41 40 39 38 37 37 36
## [20,] 44 43 42 41 40 39 38 38 37
## [21,] 44 44 43 42 41 40 39 39 38
## [22,] 45 44 43 42 42 41 40 39 39
## [23,] 45 45 44 43 42 42 41 40 39
## [24,] 46 45 44 43 43 42 41 41 40
## [25,] 46 46 45 44 43 42 42 41 41
## [26,] 47 46 46 45 44 43 43 42 42
## [27,] 48 47 46 45 45 44 44 43 42
## [28,] 48 48 47 46 45 45 44 44 43
## [29,] 49 48 47 46 46 45 45 44 43
## [30,] 49 49 48 47 46 46 45 44 44
## [31,] 50 49 48 47 47 46 46 45 44
## [32,] 50 49 48 48 47 47 46 45 44
## [33,] 51 50 49 48 48 47 46 46 45
## [34,] 51 50 49 49 48 47 47 46 45
## [35,] 51 51 50 49 48 48 47 47 46
## [36,] 52 51 50 49 49 48 48 47 46
## [37,] 52 51 51 50 49 49 48 47 46
## [38,] 53 52 51 50 50 49 49 48 47
## [39,] 54 53 52 51 51 50 49 49 48
## [40,] 55 54 53 52 52 51 50 49 49
## [41,] 55 54 53 53 52 52 51 50 49
## [42,] 56 55 54 53 53 52 52 51 49
## [43,] 56 55 54 54 53 53 52 51 50
## [44,] 56 56 55 54 53 53 52 51 50
## [45,] 57 56 55 55 54 53 52 51 50
## [46,] 58 57 56 56 55 54 53 52 51
## [47,] 60 59 58 58 57 56 55 54 53
## [48,] 60 60 60 60 59 58 57 56 55
## [49,] 60 60 60 60 60 60 59 59 58
## [50,] 60 62 62 60 60 60 60 60 61
## [51,] 61 64 67 64 60 60 60 60 60
## [52,] 63 69 76 71 65 62 60 60 60
## [53,] 65 74 88 77 70 65 61 60 60
## [54,] 64 74 84 81 73 67 62 60 60
## [55,] 60 60 65 72 71 67 62 60 60
## [56,] 60 60 60 62 63 64 62 60 60
## [57,] 60 60 60 60 61 61 61 60 60
## [58,] 60 60 60 60 60 60 60 60 59
## [59,] 60 60 60 60 60 60 60 60 60
## [60,] 60 60 60 60 60 60 60 60 58
## [61,] 60 60 60 60 60 60 60 60 57
## [62,] 60 60 60 60 60 60 60 60 56
## [63,] 60 60 60 60 60 60 60 60 55
## [64,] 60 60 60 60 60 60 60 60 54
## [65,] 60 60 60 60 60 60 60 60 53
## [66,] 60 60 60 60 60 60 60 60 54
## [67,] 60 60 60 60 60 60 60 60 54
## [68,] 60 60 60 60 60 60 60 60 54
## [69,] 60 60 60 60 60 60 60 60 54
## [70,] 60 60 60 60 60 60 60 60 55
## [71,] 60 60 60 60 60 60 60 60 57
## [72,] 60 60 60 60 60 60 60 60 59
## [73,] 60 60 60 60 60 60 60 60 60
## [74,] 60 60 60 60 60 60 60 60 60
## [75,] 60 60 60 60 60 60 60 60 60
## [76,] 60 60 60 60 60 60 60 60 60
## [77,] 60 60 60 60 60 60 60 60 60
## [78,] 60 60 60 60 60 60 60 60 60
## [79,] 60 60 60 60 60 60 60 60 60
## [80,] 60 60 60 60 60 60 60 60 60
## [81,] 60 60 60 60 60 60 60 60 60
## [82,] 60 60 60 60 60 60 60 60 60
## [83,] 60 60 60 60 60 60 60 60 60
## [,1187] [,1188] [,1189] [,1190] [,1191] [,1192] [,1193] [,1194] [,1195]
## [1,] 36 35 35 34 33 32 31 30 29
## [2,] 34 33 33 32 32 31 29 29 28
## [3,] 32 31 32 31 31 30 27 26 26
## [4,] 32 31 31 31 30 29 26 26 26
## [5,] 32 32 32 31 30 30 26 26 26
## [6,] 32 32 31 31 30 29 26 26 26
## [7,] 32 32 31 30 30 29 28 27 26
## [8,] 32 31 31 30 30 29 28 27 27
## [9,] 32 31 31 30 29 29 28 27 27
## [10,] 32 32 31 30 29 29 28 27 27
## [11,] 32 32 31 30 29 29 29 27 26
## [12,] 32 32 31 30 29 29 28 28 27
## [13,] 33 32 31 30 30 29 28 28 27
## [14,] 33 32 31 30 30 29 28 28 27
## [15,] 33 32 31 30 30 29 30 28 26
## [16,] 34 33 32 31 30 30 30 28 26
## [17,] 34 33 32 31 31 30 30 28 26
## [18,] 34 33 32 32 31 31 28 28 28
## [19,] 35 34 33 32 32 31 31 29 28
## [20,] 36 35 34 33 33 32 32 30 29
## [21,] 37 35 35 34 34 33 33 32 30
## [22,] 37 36 36 35 35 34 33 33 32
## [23,] 38 37 37 36 35 35 34 33 33
## [24,] 39 38 38 37 36 36 35 34 34
## [25,] 40 39 39 38 37 37 36 35 35
## [26,] 41 40 39 39 38 38 37 37 37
## [27,] 42 41 40 39 39 39 38 38 37
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## [39,] 47 46 46 45 45 44 43 42 42
## [40,] 48 47 47 46 46 45 44 44 43
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## [42,] 49 48 48 47 46 46 45 44 44
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## [44,] 49 49 48 47 46 45 45 44 43
## [45,] 49 49 48 48 47 46 46 44 43
## [46,] 51 50 49 49 48 47 44 44 44
## [47,] 52 52 51 51 50 49 46 46 46
## [48,] 55 55 55 54 54 53 50 49 49
## [49,] 58 59 59 59 58 57 53 52 52
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## [60,] 59 60 62 64 66 68 73 75 78
## [61,] 59 60 63 67 70 73 81 84 86
## [62,] 58 60 65 70 74 79 90 93 96
## [63,] 58 61 67 72 78 83 96 99 103
## [64,] 58 61 68 75 82 88 102 107 110
## [65,] 57 61 69 77 84 91 107 112 114
## [66,] 57 61 70 77 85 92 103 111 116
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## [68,] 57 61 69 77 84 91 105 111 115
## [69,] 57 60 66 72 78 84 96 103 107
## [70,] 57 60 63 67 72 76 84 89 94
## [71,] 58 60 62 64 67 69 72 78 82
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## [,1196] [,1197] [,1198] [,1199] [,1200] [,1201]
## [1,] 29 29 30 30 30 31
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## [7,] 26 27 29 32 39 41
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## [10,] 26 28 30 33 42 45
## [11,] 26 27 29 32 41 44
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## [14,] 26 26 26 28 31 36
## [15,] 25 25 26 28 34 37
## [16,] 25 25 26 28 34 37
## [17,] 25 25 26 28 33 36
## [18,] 29 29 30 31 33 35
## [19,] 26 26 27 29 31 35
## [20,] 27 27 28 30 32 36
## [21,] 29 29 30 32 33 37
## [22,] 32 31 31 32 36 38
## [23,] 32 32 32 33 35 38
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## [47,] 46 46 46 47 46 48
## [48,] 49 49 49 49 48 50
## [49,] 51 51 51 51 50 52
## [50,] 55 54 54 53 53 54
## [51,] 55 54 54 54 54 56
## [52,] 58 58 58 58 58 59
## [53,] 58 58 57 58 59 61
## [54,] 59 59 59 59 60 62
## [55,] 61 61 62 62 63 64
## [56,] 62 62 63 64 66 67
## [57,] 64 66 67 68 70 70
## [58,] 68 69 71 72 74 75
## [59,] 72 74 75 77 79 79
## [60,] 80 81 82 83 83 83
## [61,] 88 88 89 90 90 89
## [62,] 97 97 98 98 98 96
## [63,] 104 104 105 105 105 103
## [64,] 110 110 111 111 111 109
## [65,] 114 114 114 115 114 112
## [66,] 119 122 122 122 119 115
## [67,] 115 116 118 119 121 120
## [68,] 115 117 118 120 121 122
## [69,] 109 111 114 117 118 120
## [70,] 98 102 106 110 113 117
## [71,] 88 93 98 102 107 113
## [72,] 78 84 90 96 100 107
## [73,] 72 78 84 90 94 102
## [74,] 69 74 80 86 91 99
## [75,] 68 73 78 83 87 96
## [76,] 67 71 76 81 84 92
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## [78,] 66 70 73 77 79 87
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## [83,] 64 69 73 78 79 89
## [ reached getOption("max.print") -- omitted 1118 rows ]So, our RasterLayer object in many ways behaves like a matrix, much as a sf spatial dataframe object behaves like a data.frame.
Explore the Structure
Can we create a new RasterLayer object from a matrix?
test = raster(matrix(DEM[,], ncol = ncol(DEM), byrow = TRUE))
test## class : RasterLayer
## dimensions : 1201, 1201, 1442401 (nrow, ncol, ncell)
## resolution : 0.0008326395, 0.0008326395 (x, y)
## extent : 0, 1, 0, 1 (xmin, xmax, ymin, ymax)
## crs : NA
## source : memory
## names : layer
## values : 0, 976 (min, max)We do get a new RasterLayer! However, notice that it has no crs defined, and thus it has an incorrect extent and resolution.
Explore the Structure
You can imagine that you could then use the DEM object’s information to assign the new RasterLayer its appropriate metadata
We did a similar operation above with the unprojected point
SFhomesdata that we read in from a CSV and coerced to ansfobject.We then used the
SFtractsdata, which has a definedcrsto define thecrsof the SFhomes spatial object.
BUT, it is easier than that…
Explore the Structure
Our subsetting operation can actually take a drop = FALSE argument!
DEM[1:5, 1:5] # Bracket subsetting returns a vector## [1] 120 120 117 111 104 123 123 118 109 102 127 127 119 113 106 130 130 125 119
## [20] 113 130 131 128 123 120DEM[1:5, 1:5, drop = FALSE] #add drop=False and what do you get?## class : RasterLayer
## dimensions : 5, 5, 25 (nrow, ncol, ncell)
## resolution : 0.0008333333, 0.0008333333 (x, y)
## extent : -123.0004, -122.9963, 37.99625, 38.00042 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=NAD27 +no_defs
## source : memory
## names : layer
## values : 102, 131 (min, max)And this gives us back a new RasterLayer object! (i.e. it doesn’t drop the spatial)
In essence, this makes the subsetting operation more or less like a basic clipping function.
Explore the Structure
Check it out…
# go big to go home
test = DEM[1:500, 1:500, drop = FALSE]
plot(test)
# or
test = DEM[200:375, 525:800, drop = FALSE]
plot(test)
Explore the Structure
And now what does the @data@values slot look like in our new object now?
test@data@values## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [19] 34 60 60 71 80 79 72 60 51 54 58 60 63 64 60 62 55 57
## [37] 60 60 60 64 59 60 60 74 81 60 64 60 60 60 60 60 60 60
## [55] 60 60 60 60 60 60 60 67 63 61 86 68 66 62 61 61 60 60
## [73] 60 60 60 60 81 109 111 140 153 169 182 192 202 212 230 236 233 213
## [91] 213 181 141 114 92 79 66 61 60 60 58 54 48 43 39 37 29 21
## [109] 15 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [127] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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## [307] 60 61 61 54 49 51 54 55 55 55 56 58 60 60 60 64 60 60
## [325] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 61 78 67
## [343] 64 62 61 61 60 60 60 60 60 101 121 147 182 182 170 174 182 188
## [361] 197 205 218 243 227 208 182 153 121 113 95 83 74 67 60 60 57 52
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## [595] 58 59 59 59 60 59 59 59 60 60 60 60 60 60 60 60 60 60
## [613] 60 60 60 60 70 65 63 62 61 60 60 60 81 99 111 130 144 163
## [631] 176 181 181 180 169 171 186 189 195 193 200 196 182 158 121 112 99 89
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## [45937] 99 103 110 116 121 131 134 138 142 147 141 135 121 125 124 123 121 156
## [45955] 176 188 201 193 182 182 182 192 196 191 188 182 189 192 194 198 202 205
## [45973] 206 204 200 195 189 182 181 185 187 187 186 176 144 126 118 112 112 116
## [45991] 121 121 121 121 121 111 117 113 101 89 74 64 56 50 45 41 36 31
## [46009] 24 17 13 9 5 3 1 0 0 0 0 0 0 0 0 0 0 0
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## [46171] 37 60 60 59 59 60 60 60 60 60 60 60 60 60 60 60 60 60
## [46189] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 63
## [46207] 67 71 77 84 88 92 96 100 107 113 117 121 121 127 130 132 130 121
## [46225] 124 122 123 122 155 182 202 223 243 208 194 182 201 213 223 215 209 205
## [46243] 206 203 200 200 200 200 200 199 195 190 183 175 170 172 182 182 182 152
## [46261] 121 125 108 100 96 96 112 121 121 121 121 121 121 120 121 109 87 71
## [46279] 62 56 48 42 36 31 22 14 9 3 0 0 0 0 0 0 0 0
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## [46459] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [46477] 60 60 60 60 60 60 64 67 74 80 84 88 92 96 101 107 111 113
## [46495] 114 118 122 123 120 121 121 122 121 132 172 197 233 240 236 225 214 218
## [46513] 223 236 242 236 230 225 222 217 214 212 210 208 208 204 198 192 184 168
## [46531] 154 145 135 137 144 137 126 114 100 87 77 75 96 110 121 121 121 115
## [46549] 119 121 121 121 94 71 61 58 51 44 37 31 22 13 7 0 0 0
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## [46729] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [46747] 60 60 60 60 60 60 60 60 60 60 60 60 60 64 70 76 79 83
## [46765] 86 89 94 98 99 96 99 105 111 114 117 119 120 121 121 152 202 228
## [46783] 232 243 240 240 236 235 243 241 247 250 246 243 235 231 228 228 226 225
## [46801] 224 216 207 198 186 162 140 121 123 119 121 121 104 96 84 72 60 62
## [46819] 80 95 106 121 101 96 109 121 121 121 89 60 62 55 50 46 39 33
## [46837] 23 14 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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## [46999] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [47017] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [47035] 60 60 64 70 74 76 79 82 85 86 86 83 85 89 98 108 113 119
## [47053] 121 121 132 168 233 241 243 243 243 243 242 241 243 243 254 263 271 262
## [47071] 250 242 241 249 244 247 245 236 222 207 188 162 128 120 116 112 99 80
## [47089] 80 76 66 62 63 61 65 78 85 81 78 69 85 99 121 121 85 73
## [47107] 61 56 51 46 41 35 25 16 9 4 0 0 0 0 0 0 0 0
## [47125] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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## [47233] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [47251] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [47269] 0 0 0 0 0 14 60 60 61 61 61 61 60 60 60 66 67 64
## [47287] 60 66 63 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [47305] 60 60 60 60 60 60 60 60 60 64 67 69 71 72 74 74 71 69
## [47323] 70 72 87 102 111 121 121 121 142 170 243 243 242 243 243 243 243 243
## [47341] 243 243 264 285 304 288 273 266 266 267 269 262 255 247 243 220 196 182
## [47359] 121 114 112 101 86 63 60 60 62 60 61 61 60 60 60 60 60 62
## [47377] 60 76 99 99 76 67 63 59 55 49 44 38 29 19 13 7 1 0
## [47395] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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## [47503] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [47521] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [47539] 0 0 0 0 0 0 0 0 0 0 0 12 60 60 61 64 65 64
## [47557] 60 60 72 75 77 75 75 74 71 67 62 60 60 60 60 60 60 60
## [47575] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 61 62
## [47593] 63 64 64 63 61 60 60 60 74 93 103 111 118 121 136 168 213 238
## [47611] 242 243 243 246 249 252 261 269 277 296 302 304 297 290 288 289 295 282
## [47629] 268 253 243 228 200 182 138 121 122 115 96 69 62 60 60 60 60 61
## [47647] 60 60 60 60 60 60 60 60 76 67 63 63 61 61 60 55 49 42
## [47665] 32 22 16 10 4 0 0 0 0 0 0 0 0 0 0 0 0 0
## [47683] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [47701] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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## [47809] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
## [47827] 40 60 63 67 74 74 64 77 82 86 88 87 87 84 79 74 69 64
## [47845] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [47863] 60 60 60 60 60 60 60 60 61 60 60 60 60 60 67 85 95 103
## [47881] 111 117 121 148 170 182 243 243 243 250 267 280 304 294 290 300 304 304
## [47899] 304 304 302 304 303 304 286 261 243 227 195 172 160 150 128 121 103 80
## [47917] 66 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 61
## [47935] 60 60 60 60 57 47 36 25 18 12 5 0 0 0 0 0 0 0
## [47953] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [47971] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [47989] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48007] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48025] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48043] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48061] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48079] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48097] 0 0 0 0 0 0 32 60 68 79 94 92 85 90 95 97 99 99
## [48115] 98 92 87 81 75 69 62 60 60 60 60 60 60 60 60 60 60 60
## [48133] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [48151] 60 60 70 80 89 97 105 113 119 134 157 168 177 213 233 251 266 277
## [48169] 296 304 302 303 304 304 304 304 304 304 304 304 304 267 243 233 207 182
## [48187] 168 161 142 121 113 91 79 69 60 60 60 60 60 60 60 60 60 60
## [48205] 60 60 60 60 60 60 60 60 60 60 54 50 38 27 20 13 7 0
## [48223] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48241] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48259] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48277] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48295] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48313] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48331] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48349] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48367] 0 0 0 0 0 0 0 0 0 0 0 0 29 60 77 96 121 105
## [48385] 101 104 106 108 110 112 110 102 96 89 81 74 65 60 60 60 60 60
## [48403] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [48421] 60 60 60 60 60 60 60 60 70 80 86 93 100 108 118 130 145 155
## [48439] 163 172 182 230 255 259 275 291 304 304 304 304 304 304 304 304 304 304
## [48457] 295 272 247 243 221 201 189 183 169 134 120 103 92 82 68 60 60 60
## [48475] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 54 47
## [48493] 39 29 22 16 9 4 0 0 0 0 0 0 0 0 0 0 0 0
## [48511] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48529] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48547] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [48565] 0 0 0 0 0 0 0 0 0 0 0 0Explore the Structure
That makes sense, because our test object didn’t come from a file, so R didn’t leave its data on disk.
test@data@inmemory## [1] TRUEtest@data@fromdisk## [1] FALSEExplore the data values
Descriptive raster statistics are called global raster operations.
# Quick summary stats
summary(DEM)## Warning in .local(object, ...): summary is an estimate based on a sample of 1e+05 cells (6.93% of all cells)## san_francisco.e
## Min. 0
## 1st Qu. 0
## Median 0
## 3rd Qu. 75
## Max. 961
## NA's 0summary(DEM[,])## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 0.00 73.18 75.00 976.00freq(DEM)## value count
## [1,] 0 897077
## [2,] 1 2623
## [3,] 2 2340
## [4,] 3 2666
## [5,] 4 2075
## [6,] 5 2237
## [7,] 6 1988
## [8,] 7 2390
## [9,] 8 2066
## [10,] 9 1958
## [11,] 10 2281
## [12,] 11 1935
## [13,] 12 1989
## [14,] 13 1874
## [15,] 14 2237
## [16,] 15 1804
## [17,] 16 2006
## [18,] 17 2177
## [19,] 18 1711
## [20,] 19 1853
## [21,] 20 1764
## [22,] 21 2002
## [23,] 22 1759
## [24,] 23 1824
## [25,] 24 2010
## [26,] 25 1708
## [27,] 26 1825
## [28,] 27 1708
## [29,] 28 2153
## [30,] 29 1800
## [31,] 30 2037
## [32,] 31 1798
## [33,] 32 2336
## [34,] 33 1991
## [35,] 34 1745
## [36,] 35 2235
## [37,] 36 1757
## [38,] 37 1920
## [39,] 38 1924
## [40,] 39 2373
## [41,] 40 2059
## [42,] 41 1950
## [43,] 42 2325
## [44,] 43 1919
## [45,] 44 2039
## [46,] 45 2008
## [47,] 46 2313
## [48,] 47 1941
## [49,] 48 2210
## [50,] 49 2494
## [51,] 50 2219
## [52,] 51 2450
## [53,] 52 2365
## [54,] 53 3026
## [55,] 54 2528
## [56,] 55 2863
## [57,] 56 3663
## [58,] 57 3616
## [59,] 58 3822
## [60,] 59 4391
## [61,] 60 38791
## [62,] 61 2348
## [63,] 62 1518
## [64,] 63 1114
## [65,] 64 1180
## [66,] 65 980
## [67,] 66 885
## [68,] 67 972
## [69,] 68 753
## [70,] 69 858
## [71,] 70 747
## [72,] 71 921
## [73,] 72 790
## [74,] 73 695
## [75,] 74 814
## [76,] 75 693
## [77,] 76 741
## [78,] 77 618
## [79,] 78 787
## [80,] 79 633
## [81,] 80 650
## [82,] 81 879
## [83,] 82 641
## [84,] 83 660
## [85,] 84 615
## [86,] 85 782
## [87,] 86 609
## [88,] 87 696
## [89,] 88 647
## [90,] 89 782
## [91,] 90 693
## [92,] 91 805
## [93,] 92 713
## [94,] 93 585
## [95,] 94 711
## [96,] 95 604
## [97,] 96 723
## [98,] 97 701
## [99,] 98 675
## [100,] 99 772
## [101,] 100 612
## [102,] 101 802
## [103,] 102 623
## [104,] 103 783
## [105,] 104 601
## [106,] 105 710
## [107,] 106 879
## [108,] 107 685
## [109,] 108 723
## [110,] 109 735
## [111,] 110 817
## [112,] 111 812
## [113,] 112 802
## [114,] 113 948
## [115,] 114 840
## [116,] 115 919
## [117,] 116 841
## [118,] 117 1085
## [119,] 118 1001
## [120,] 119 1253
## [121,] 120 1601
## [122,] 121 33373
## [123,] 122 2350
## [124,] 123 1274
## [125,] 124 1181
## [126,] 125 897
## [127,] 126 964
## [128,] 127 808
## [129,] 128 962
## [130,] 129 819
## [131,] 130 694
## [132,] 131 954
## [133,] 132 623
## [134,] 133 716
## [135,] 134 658
## [136,] 135 729
## [137,] 136 606
## [138,] 137 724
## [139,] 138 709
## [140,] 139 563
## [141,] 140 629
## [142,] 141 602
## [143,] 142 847
## [144,] 143 516
## [145,] 144 562
## [146,] 145 728
## [147,] 146 553
## [148,] 147 634
## [149,] 148 586
## [150,] 149 686
## [151,] 150 591
## [152,] 151 618
## [153,] 152 821
## [154,] 153 660
## [155,] 154 590
## [156,] 155 581
## [157,] 156 636
## [158,] 157 553
## [159,] 158 644
## [160,] 159 565
## [161,] 160 643
## [162,] 161 557
## [163,] 162 836
## [164,] 163 671
## [165,] 164 562
## [166,] 165 610
## [167,] 166 549
## [168,] 167 787
## [169,] 168 596
## [170,] 169 658
## [171,] 170 825
## [172,] 171 626
## [173,] 172 891
## [174,] 173 670
## [175,] 174 835
## [176,] 175 731
## [177,] 176 842
## [178,] 177 795
## [179,] 178 1046
## [180,] 179 978
## [181,] 180 1094
## [182,] 181 1888
## [183,] 182 25873
## [184,] 183 2049
## [185,] 184 1021
## [186,] 185 1042
## [187,] 186 820
## [188,] 187 844
## [189,] 188 901
## [190,] 189 734
## [191,] 190 754
## [192,] 191 607
## [193,] 192 950
## [194,] 193 576
## [195,] 194 720
## [196,] 195 716
## [197,] 196 613
## [198,] 197 624
## [199,] 198 647
## [200,] 199 686
## [201,] 200 543
## [202,] 201 587
## [203,] 202 795
## [204,] 203 607
## [205,] 204 550
## [206,] 205 558
## [207,] 206 698
## [208,] 207 468
## [209,] 208 601
## [210,] 209 514
## [211,] 210 636
## [212,] 211 582
## [213,] 212 551
## [214,] 213 1027
## [215,] 214 533
## [216,] 215 531
## [217,] 216 536
## [218,] 217 591
## [219,] 218 563
## [220,] 219 552
## [221,] 220 596
## [222,] 221 482
## [223,] 222 557
## [224,] 223 778
## [225,] 224 577
## [226,] 225 539
## [227,] 226 582
## [228,] 227 626
## [229,] 228 664
## [230,] 229 532
## [231,] 230 552
## [232,] 231 726
## [233,] 232 499
## [234,] 233 791
## [235,] 234 542
## [236,] 235 727
## [237,] 236 774
## [238,] 237 694
## [239,] 238 826
## [240,] 239 719
## [241,] 240 771
## [242,] 241 946
## [243,] 242 1636
## [244,] 243 18291
## [245,] 244 1212
## [246,] 245 863
## [247,] 246 683
## [248,] 247 665
## [249,] 248 587
## [250,] 249 663
## [251,] 250 595
## [252,] 251 609
## [253,] 252 585
## [254,] 253 705
## [255,] 254 540
## [256,] 255 532
## [257,] 256 571
## [258,] 257 490
## [259,] 258 502
## [260,] 259 660
## [261,] 260 411
## [262,] 261 505
## [263,] 262 438
## [264,] 263 668
## [265,] 264 455
## [266,] 265 466
## [267,] 266 416
## [268,] 267 575
## [269,] 268 484
## [270,] 269 431
## [271,] 270 488
## [272,] 271 421
## [273,] 272 444
## [274,] 273 437
## [275,] 274 874
## [276,] 275 479
## [277,] 276 411
## [278,] 277 551
## [279,] 278 411
## [280,] 279 465
## [281,] 280 412
## [282,] 281 499
## [283,] 282 413
## [284,] 283 436
## [285,] 284 721
## [286,] 285 425
## [287,] 286 477
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## [956,] 976 1maxValue(DEM)## [1] 32767minValue(DEM)## [1] -32768res(DEM)## [1] 0.0008333333 0.0008333333Plot Data Values
Histogram is a great way to view distribution of data.
hist(DEM[,],
main = "Distribution of elevation values",
xlab = "Elevation (meters)", ylab = "Frequency",
col = "springgreen")
Read Raster into Memory
If you have a small raster and/or lots of memory…
# proceed with caution!
DEM2 <- readAll(DEM)
inMemory(DEM)## [1] FALSEinMemory(DEM2)## [1] TRUEhist(DEM,
main = "Distribution of elevation values",
xlab = "Elevation (meters)", ylab = "Frequency",
col = "springgreen")## Warning in .hist1(x, maxpixels = maxpixels, main = main, plot = plot, ...): 7%
## of the raster cells were used. 100000 values used.
CRS Transformations
Check the CRS (aka projection) of the DEM raster data.
Transform (or reproject) the CRS of the SF tracts vector data to match it.
We can transform the CRS of an sf object with sf::st_transform
#check out its CRS
st_crs(DEM)## Coordinate Reference System:
## User input: NAD27 (with axis order normalized for visualization)
## wkt:
## GEOGCRS["NAD27 (with axis order normalized for visualization)",
## DATUM["North American Datum 1927",
## ELLIPSOID["Clarke 1866",6378206.4,294.978698213898,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## CS[ellipsoidal,2],
## AXIS["geodetic longitude (Lon)",east,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433,
## ID["EPSG",9122]]],
## AXIS["geodetic latitude (Lat)",north,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433,
## ID["EPSG",9122]]]]#or just its proj4string
proj4string(DEM)## [1] "+proj=longlat +datum=NAD27 +no_defs"# Reproject tracts to our DEM projection
SFtracts_NAD27 = st_transform(SFtracts_NAD83, st_crs(DEM))
st_crs(SFtracts_NAD27)## Coordinate Reference System:
## User input: NAD27 (with axis order normalized for visualization)
## wkt:
## GEOGCRS["NAD27 (with axis order normalized for visualization)",
## DATUM["North American Datum 1927",
## ELLIPSOID["Clarke 1866",6378206.4,294.978698213898,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## CS[ellipsoidal,2],
## AXIS["geodetic longitude (Lon)",east,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433,
## ID["EPSG",9122]]],
## AXIS["geodetic latitude (Lat)",north,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433,
## ID["EPSG",9122]]]]Plot Raster and a Vector objects
Plot the DEM with the SF Tracts overlayed
# Why do we set the value for ext?
plot(DEM, ext=extent(SFtracts_NAD27))
# Overlay the tracts
plot(SFtracts_NAD27$geometry, add=T)
CRS Transformations
Above, we reprojected the vector sf object SFtracts to a new object with the same CRS as the DEM raster.
Similarly, you can reproject the DEM with raster::projectRaster
- Note, the syntax is similar to
sf::st_transform
#Transform the CRS
DEM_NAD83 = projectRaster(DEM, projectExtent(DEM, st_crs(SFtracts_NAD83)))## Warning in wkt(pto): CRS object has no comment## Warning in rgdal::rawTransform(projfrom, projto, nrow(xy), xy[, 1], xy[, : Using
## PROJ not WKT2 strings## Error in rgdal::rawTransform(projfrom, projto, nrow(xy), xy[, 1], xy[, : target crs creation failed: generic error of unknown originCRS Transformations
Oops! What went wrong?
That’s not a very informative error message…
Let’s read the docs!
?projectRasterCRS Transformations
Looks like projectRaster requires the crs argument to be an object of type (uppercase) ‘CRS’ class".
Is it?
class(st_crs(SFtracts_NAD83))## [1] "crs"CRS Transformations
We need to be careful when working between the raster and sf packages, because raster is an older package and still depends on sp.
This (lowercase) crs class is defined by the sf package and it is returned by sf::st_crs(SFtracts_NAD83) because SFtracts_NAD83 is an sf object. Picky!
This (uppercase) CRS class is defined by the sp/raster package and is used to transform the CRS of a raster or sp object.
However, we can actually just extract the proj4string from our sf crs-class object and use that as our argument instead!
#Transform the CRS
# Check proj4string
st_crs(SFtracts_NAD83)$proj4string## [1] "+proj=longlat +datum=NAD83 +no_defs"# Use it to reproject the DEM
DEM_NAD83 = projectRaster(DEM, projectExtent(DEM, st_crs(SFtracts_NAD83)$proj4string))
# plot it
plot(DEM_NAD83, ext=extent(SFtracts_NAD83))
plot(SFtracts_NAD83$geometry, col=NA, add=T)
CRS Transformations
Now, we can check equivalence of the CRSs
# Compare the CRS of these objects using sf::st_crs
# NAD27 (epsg = 4267)
st_crs(SFtracts_NAD27) == st_crs(DEM)## [1] TRUE# NAD83 (epsg = 4269)
st_crs(DEM_NAD83) == st_crs(SFtracts_NAD83)## [1] TRUEAbout the sp package
As we mentioned in Part I, sp was for a long time the primary geospatial package in R.
sf has now eclipsed this package (along with the ‘rgdal’ and ‘rgeos’ packages).
However, as you can see, not all geospatial packages have made the transition already.
sp package
You may sometimes run into issues such as the one we just experienced, where you can find an easy workaround.
Other times, however, you may actually need to work with sp objects instead of sf ones.
Luckily, this is easy!
sp package
To convert from sf to sp, sf provides the as_Spatial function.
Let’s convert SFhomes15_sf, then look at its string representation.
Note that it looks very similar to the metadata of a raster object.
SFhomes15_sp <- as_Spatial(SFhomes15_NAD83)
SFhomes15_sp## class : SpatialPointsDataFrame
## features : 5849
## extent : -122.5107, -122.3696, 37.70821, 37.80612 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=NAD83 +no_defs
## variables : 17
## names : FiscalYear, SalesDate, Address, YearBuilt, NumBedrooms, NumBathrooms, NumRooms, NumStories, NumUnits, AreaSquareFeet, ImprovementValue, LandValue, Neighborhood, Location, SupeDistrict, ...
## min values : 2015, 2015-01-02, 0000 0000 0000, 24, 0, 0, 0, 0, 0, 0, 0, 0, , (37.7082125474599, -122.456157054616), 1, ...
## max values : 2015, 2015-12-31, S000 3016 SACRAMENTO ST0000, 2016, 13, 13, 43, 75, 9, 40000, 1979737, 2614268, Western Addition, (37.8061200328565, -122.419485868976), 11, ...sp package
And look at its structure, which is also similar to that of the DEM raster.
str(SFhomes15_sp)sp package
That makes sense, because the raster and sp packages are designed to feel as standardized and consistent as possible.
There are differences, however!
Some are just stylistic:
- sp
@bboxinstead of raster@extent - sp
@proj4stringinstead of raster@crs
Some come from the difference between the vector and raster data models:
sp vector objects have - no dimensions attribute - no resolution (this is a concept for vector data, but is not key metadata) - a @data slot is a data.frame (a.k.a. an “attribute table”)
sp package
sp creates objects that pertain to any of a number of classes, which conform to the Spatial*DataFrame convention:
SpatialPointsDataFrameSpatialLinesDataFrameSpatialPolygonsDataFrame- etc.
sp Spatial objects can then be transformed, subsetted, analyzed, and plotted, using a variety of packages that may not be compatible (yet?) with sf.
Here’s a plot:
plot(SFhomes15_sp)
sp package
And if you need to convert from sp to sf, there’s a function for that too (which we already saw in Part 1!).
SFhomes15_sfagain <- st_as_sf(SFhomes15_sp)
plot(SFhomes15_sfagain$geometry)
plot(SFhomes15_sfagain['totvalue'])
sp package
We will not go into any further detail on sp in this workshop.
However, if you find you need to learn more then please visit our former R geospatial workshop, which is based on sp.
(It uses the same data and runs more or less the same operations as this workshop, so the comparison with this workshop should highlight all the differences between sf and sp.)
Cropping Rasters
Since the raster data covers a larger area than our vector data / area of interest, we can clip, or crop, it using the raster::crop function.
# clip the NAD83 CRS version of the rasters to SFtracts
DEM_NAD83_crop <- crop(DEM_NAD83, SFtracts_NAD83)
# Clip the NAD27 CRS version
DEM_crop <- crop(DEM, SFtracts_NAD27)Plot Cropped Raster data
You can plot raster and vector
plot(DEM_NAD83_crop)
Plot Raster & Vector Data
Here we plot the NAD83 CRS version.
# plot together
plot(DEM_NAD83_crop)
plot(SFtracts_NAD83$geometry, add=T, border="black")
Masking Raster Data
Notice that the clipping (or cropping) operation reduced our dataset to just the extent of the census-tract dataset.
But it still left us with values outside of the census tracts themselves (because they are areas outside the city of San Francisco, eg Marin & Tiburon).
Masking Raster Data
For some purposes, we may want to get rid of those values as well.
We can do this with an operation called masking.
DEM_NAD83_crop_masked = mask(DEM_NAD83_crop, SFtracts_NAD83)Masking Raster Data
Here’s what that gives us, compared to the unmasked object:
# What's different?
DEM_NAD83_crop_masked## class : RasterLayer
## dimensions : 187, 224, 41888 (nrow, ncol, ncell)
## resolution : 0.0008333663, 0.0008333239 (x, y)
## extent : -122.5148, -122.3281, 37.70781, 37.86364 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=NAD83 +no_defs
## source : memory
## names : san_francisco.e
## values : 0, 269.8798 (min, max)DEM_NAD83_crop## class : RasterLayer
## dimensions : 187, 224, 41888 (nrow, ncol, ncell)
## resolution : 0.0008333663, 0.0008333239 (x, y)
## extent : -122.5148, -122.3281, 37.70781, 37.86364 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=NAD83 +no_defs
## source : memory
## names : san_francisco.e
## values : 0, 303.9921 (min, max)Masking Raster Data
Still a rectangular grid of cells (because a raster will always be rectangular).
Still has the same nrow and ncol as the unmasked object.
What masking did was to set the cells that lie outside our dataset to NAs.
Masking Raster Data
plot(DEM_NAD83_crop_masked)
plot(st_geometry(SFtracts_NAD83), add = T, col = NA)
Plotting rasters in tmap
We can make an interactive plot using tmap
my_map <- tm_shape(DEM_NAD83_crop_masked) +
tm_raster() +
tm_shape(SFtracts_NAD83) +
tm_borders()
# Set mode to interactive
tmap_mode("view")View Map
my_mapWriting Raster Data
And now that we’ve manipulated our data as desired, we can write it to disk if we like!
# write our reprojected, cropped data to the data directory, using the Geotiff format
# (and allow R to overwrite if file already exists)
writeRaster(DEM_NAD83_crop_masked,
filename = here("outdata",
"DEM_reproject_crop.tif"),
format = "GTiff",
overwrite = T)Section 2: Raster Operations and Spatial Analysis
Challenge section
This section will feature a number of challenges, to get you practicing some of the material we’ve already covered today.
Extract elevation values
We can use the raster::extract function to get the elevation values for each tract.
# get the elevation for every cell in each of the census tracts
elev <- extract(DEM_NAD83_crop, SFtracts_NAD83)
#what did that give us?
head(elev)## [[1]]
## [1] 55.99014 57.99510 57.99514 58.99756 58.99757 58.99759 59.99757 59.99758
## [9] 59.99759 59.99761 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [17] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [25] 59.99361 60.00000 60.00000
##
## [[2]]
## [1] 59.00234 59.00237 59.00236 59.00234 58.99395 59.00000 58.99399 58.00234
## [9] 57.99628 58.00235 58.00233 57.99399 56.99629
##
## [[3]]
## [1] 57.99226 57.99485 57.99486 57.99490 58.99742 58.99743 58.99744 58.99745
## [9] 59.99743 59.99744 59.99745 59.99746 60.00000 60.00000 60.00000 60.00000
## [17] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [25] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [33] 60.00000 60.00000 60.00000
##
## [[4]]
## [1] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [26] 60 60 60 60 60 60 60 60 60 60
##
## [[5]]
## [1] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [26] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
##
## [[6]]
## [1] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [26] 60 60 60 60 60 60 60 60 60 60 60tail(elev)## [[1]]
## [1] 182.00000 181.98596 178.99049 175.98344 171.98093 166.96416 157.95902
## [8] 146.96586 137.00367 134.04383 182.00000 181.98131 177.98823 174.98817
## [15] 171.96701 164.94782 152.94492 138.95619 126.01034 123.02937 182.00000
## [22] 182.00000 182.00000 181.99996 181.99082 181.98403 181.92564 170.91575
## [29] 155.91761 139.90771 121.01113 121.00922 121.99968 121.01580 182.00000
## [36] 182.00000 182.02765 188.05093 201.94500 199.92646 192.94707 186.96988
## [43] 182.91185 169.91199 157.92185 149.84558 130.93040 121.00220 121.00001
## [50] 121.00219 121.02617 181.00001 181.00687 182.00000 182.00000 182.17922
## [57] 220.95232 226.89219 215.89409 200.94001 191.96072 185.97911 182.96614
## [64] 181.94652 181.82981 160.83904 140.86112 121.00000 121.00000 121.00005
## [71] 121.01093 181.00451 181.99768 182.05670 195.05197 213.03383 235.90894
## [78] 242.94993 242.90828 230.85040 205.93303 193.96291 186.98375 183.98841
## [85] 182.00000 181.99978 181.90644 171.83727 151.80426 124.97227 121.00000
## [92] 121.00000 181.99769 182.10825 205.99457 217.06765 242.99533 256.89286
## [99] 243.99315 242.99988 242.81146 207.93531 194.96525 187.97450 182.99753
## [106] 182.00000 182.00000 181.99990 181.97798 181.73581 139.87734 121.00000
## [113] 121.00000 196.02138 207.98975 219.01986 230.02933 243.07729 259.92478
## [120] 244.96120 236.94025 220.98470 206.94682 194.96296 186.98363 182.99534
## [127] 182.00000 182.00000 182.00000 181.95767 172.90111 147.88793 212.03919
## [134] 229.01462 242.94518 242.92990 234.06133 242.97024 228.00181 219.99691
## [141] 210.98100 201.95589 189.97415 181.96480 172.01956 171.02411 171.01935
## [148] 169.99335 163.01290 156.95428 139.96037 127.96681 120.97625 213.08697
## [155] 233.03120 242.00676 242.87851 216.01376 210.06066 207.02892 203.01062
## [162] 196.98544 186.99194 177.96673 164.99125 155.03263 154.03711 154.01836
## [169] 150.01527 144.00351 135.99335 124.99434 116.99506 110.98331 102.97523
## [176] 92.03255 90.00322 182.09442 189.04022 189.02659 187.99256 181.93335
## [183] 164.95064 147.98665 137.04390 138.03018 137.02751 135.01370 130.98123
## [190] 121.03666 121.93597 106.95531 92.98135 80.94683 60.06702 60.06250
## [197] 60.06754 65.02899 174.05138 178.04020 181.88150 155.92827 135.97573
## [204] 125.04908 130.01732 130.01046 129.00358 126.98057 121.00001 120.93184
## [211] 105.93164 90.93354 75.98197 69.93183 60.00000 60.00005
##
## [[2]]
## [1] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [9] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [17] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [25] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [33] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [41] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [49] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [57] 60.00000 60.00524 61.00248 60.00000 60.00000 60.00000 60.00521 61.00769
## [65] 63.00496
##
## [[3]]
## [1] 60.00000 59.99425 58.99424 57.98269 54.99071 60.00000 60.00000 60.00000
## [9] 60.00000 60.00000 60.00000 60.00000 60.00000 59.99427 58.98852 56.99075
## [17] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 59.99428
## [25] 58.98854 60.00000 60.00000 60.00000 60.00000 60.00000
##
## [[4]]
## [1] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [6] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [11] 0.000000000 0.000000000 0.000000000 2.993618216 1.987208911
## [16] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [21] 0.000000000 0.000000000 3.987304908 1.995644241 0.995608841
## [26] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [31] 0.000000000 0.000000000 3.995695269 2.995659892 1.993646330
## [36] 0.993632569 0.000000000 0.000000000 0.000000000 0.000000000
## [41] 0.000000000 0.000000000 0.000000000 0.000000000 5.995746297
## [46] 4.989425350 2.995701060 1.995678442 0.995655824 0.001973961
## [51] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [56] 0.000000000 0.000000000 0.000000000 6.989517959 4.989494260
## [61] 2.997730552 1.995706849 0.995684231 0.001974601 0.000000000
## [66] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [71] 0.000000000 0.000000000 0.000000000 6.995803113 5.989537803
## [76] 3.989501420 1.995735254 0.995712635 0.001975240 0.000000000
## [81] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [86] 0.000000000 0.000000000 0.000000000 0.000000000 12.991844011
## [91] 10.997945894 9.989715842 6.997851539 5.995808898 4.989557644
## [96] 2.989521261 0.995741039 0.001975877 0.000000000 0.000000000
## [101] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [106] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [111] 14.983713962 11.989795798 9.995905166 8.989723023 6.995859923
## [116] 5.989662776 3.997830176 2.991584121 0.997754781 0.001976512
## [121] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [126] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [131] 0.000000000 0.000000000 0.000000000 10.989815636 8.989791773
## [136] 6.997909617 5.995865703 4.989670087 2.995820461 1.989597317
## [141] 0.001977145 0.000000000 0.000000000 0.000000000 0.000000000
## [146] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [151] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [156] 9.983744065 6.997938651 5.989775114 3.997888139 2.997844296
## [161] 1.989665874 0.003955554 0.000000000 0.000000000 0.000000000
## [166] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [171] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [176] 0.000000000 0.000000000 10.983828055 7.991877859 5.989831281
## [181] 3.997904776 2.989758452 0.997854160 0.003956814 0.000000000
## [186] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [191] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [196] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [201] 11.998059621 10.989960279 8.991934709 6.983811679 3.997933802
## [206] 2.989814616 0.997870898 0.001979035 0.000000000 0.000000000
## [211] 0.000000000 0.000000000 0.006187586 0.991860510 0.000000000
## [216] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [221] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [226] 0.000000000 12.996034834 11.987971488 9.989967741 7.989931350
## [231] 5.983833246 2.989870778 0.997899919 0.001979662 0.000000000
## [236] 0.000000000 0.000000000 0.006146028 1.004212280 1.996134620
## [241] 1.991870799 0.998079023 0.991872887 0.000000000 0.000000000
## [246] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [251] 0.000000000 0.000000000 0.000000000 14.988042359 12.988027080
## [256] 10.996018083 9.987959750 7.981910504 4.983867124 1.989878393
## [261] 0.001980287 0.000000000 0.000000000 0.006104469 1.010279554
## [266] 2.994167628 2.996133424 2.998069596 2.991893132 1.991900079
## [271] 0.993787153 0.000000000 0.000000000 0.000000000 0.000000000
## [276] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [281] 0.000000000 16.988098006 14.994023029 13.986005686 11.991979309
## [286] 10.985968326 8.985937543 6.977895543 3.977884005 0.991966778
## [291] 0.000000000 0.006076702 1.016325891 4.000282071 4.996120340
## [296] 4.990006175 3.998077879 3.991915465 2.991910555 1.991905644
## [301] 0.991912455 0.000000000 0.000000000 0.000000000 0.000000000
## [306] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [311] 17.992004235 16.984035075 14.991994460 13.989981549 12.983993475
## [316] 10.989977412 9.975960742 6.981967354 4.986049630 3.992132141
## [321] 3.998242186 5.004391630 6.994190643 6.990032802 5.991947622
## [326] 4.998086164 4.991937800 3.991932889 2.991927978 1.985736197
## [331] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [336] 0.000000000 0.000000000 0.000000000 0.000000000 19.990000348
## [341] 18.989992243 17.987987567 16.988000368 15.988001194 14.986031868
## [346] 13.980036098 11.978079520 9.972086964 6.994123969 7.000211107
## [351] 8.000263229 8.990059432 7.991974870 6.991969958 5.991976727
## [356] 4.993856830 3.993843065 2.993829300 1.993803969 0.991952027
## [361] 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## [366] 21.990030982 20.995945561 20.988026491 19.993977514 19.986057424
## [371] 18.992044891 18.978132329 16.972155669 13.974106066 10.992198449
## [376] 10.998280391 11.986232423 10.990078297 0.993815818 0.000000000
## [381] 23.995944485 23.993961174 23.988065419 22.994014311 22.994029060
## [386] 22.986138090 21.982139212 19.976147072 16.982125555 14.992231612
## [391] 14.992278694 14.988180597 13.982144994 0.993829864 27.991945982
## [396] 27.991981407 27.992005040 27.990065319 27.990109598 1.985862713
##
## [[5]]
## [1] 61.99999 61.99331 61.00000 61.00000 62.99335 62.00000 62.00000 61.99999
## [9] 61.99333 61.00000 60.99999 60.00000 60.00000 63.99337 62.99999 62.99822
## [17] 62.99336 62.00000 61.99999 61.99334 61.00000 60.99506 60.00000 60.00000
## [25] 60.00000 60.00000 60.00000 64.99339 63.99339 63.00000 62.99999 62.99338
## [33] 62.00000 61.99999 61.99336 60.99999 60.99829 60.99335 60.00000 60.00000
## [41] 60.00000 60.00000 64.99519 63.99999 63.99823 63.99340 62.99999 62.99826
## [49] 62.99339 61.99999 61.99338 61.00000 60.99999 60.99336 60.00000 60.00000
## [57] 60.00000 60.00000 65.99999 65.99343 64.99344 64.00000 63.99999 63.99342
## [65] 63.00000 62.99513 62.00000 61.99510 61.00000 61.00000 60.99506 60.00000
## [73] 60.00000 60.00000 60.00000 60.00000 67.99346 66.99822 66.98869 64.99521
## [81] 64.00000 64.00000 63.99999 63.99344 62.99514 62.00000 61.99511 61.00000
## [89] 61.00000 60.99507 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [97] 60.00000 60.00000 60.00000 60.00000 68.98876 67.00000 66.99523 65.99347
## [105] 64.99348 64.00000 64.00000 63.99517 62.99999 62.99345 61.99513 61.00000
## [113] 61.00000 60.99508 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [121] 60.00000 60.00000 60.00000 68.99527 67.99351 66.99525 65.99524 64.99999
## [129] 64.99349 64.00000 63.99999 63.99348 62.99515 61.99514 61.00000 61.00000
## [137] 60.99510 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [145] 60.00000 60.00000 69.99353 68.98881 66.99526 65.99999 65.99352 64.99522
## [153] 64.00000 64.00000 63.99518 62.99517 61.99515 61.00000 61.00000 60.99511
## [161] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [169] 70.99999 70.98887 68.99528 67.99354 66.99355 65.99525 64.99999 64.99353
## [177] 64.00000 63.99520 62.99518 61.99999 61.99351 61.00000 60.99999 60.99349
## [185] 60.00000 60.00000 60.00000 60.00000 70.99531 69.99357 68.98887 66.99528
## [193] 65.99526 65.00000 64.99524 64.00000 63.99521 62.99520 62.00000 61.99517
## [201] 61.00000 60.00000 60.00000 69.99065 67.99702 66.99529 65.99528 64.99527
## [209] 64.00167 63.99525 62.99689 62.00165 62.00000 61.99518 61.00000 69.98601
## [217] 66.99236 64.99871 64.00337 63.99696 61.00164 61.00162 60.99519 68.99417
## [225] 66.99582 64.98941 62.00507 62.00336 62.00334 65.99588 63.99583 62.00041
## [233] 60.99703 60.00335 62.99244 61.00168 60.99535 60.00000
##
## [[6]]
## [1] 0.000000000 0.004923311 1.011680391 4.017325750 10.040508873
## [6] 0.000000000 0.000000000 0.014686530 3.000439447 4.997401858
## [11] 7.020372484 13.030444855 0.000000000 0.000000000 0.000000000
## [16] 0.009707838 2.008321090 4.994148317 6.997328212 8.997391305
## [21] 11.017207200 17.022292766 0.000000000 0.000000000 0.000000000
## [26] 0.019304468 4.001983708 6.998943097 9.989278636 10.997333087
## [31] 12.997396180 15.012246839 20.030222830 28.012455744 33.015615547
## [36] 12.973116779 15.930301916 11.957388253 10.960683931 9.990897132
## [41] 11.994102468 13.997259707 15.989363982 16.997401063 19.012194185
## [46] 24.027070038 32.012403095 37.007571334 41.015665451 46.015761021
## [51] 51.005901427 54.017014431 58.010025472 59.997006079 60.000000000
## [56] 60.000000000 60.000000000 60.000000000 60.000000000 60.000000000
## [61] 42.876686684 36.866966211 22.946276374 18.960518886 15.986091513
## [66] 16.994100461 18.989332972 19.992474523 20.997405953 59.922606775
## [71] 54.833808322 31.938336785 24.966848576 21.981314095 21.989301969
## [76] 22.992444212 60.992052672 59.879646307 37.947843825 30.962170436
## [81] 26.984457281 26.989314242 27.984560984What is the output?
Check out the data in the elev object
length(elev)## [1] 195nrow(SFtracts_NAD83)## [1] 195It’s a vector of the elevations for all the raster cells within each census tract!
Let’s take a closer look
# Large census tract at row 100
plot(SFtracts_NAD83$geometry)
plot(SFtracts_NAD83[100,]$geometry, add=T, col="red")
# Lots of cells
elev[100]## [[1]]
## [1] 0.0000000 0.0000000 11.9694923 7.9825166 0.0000000 0.0000000
## [7] 0.0000000 0.0000000 15.9847869 13.9760609 10.9738777 7.9760281
## [13] 4.9694673 0.9912873 0.0000000 0.0000000 0.0000000 0.0000000
## [19] 0.0000000 19.9783876 16.9848376 14.9783228 11.9847861 9.9695773
## [25] 5.9782114 2.9826049 0.9913046 0.0000000 0.0000000 0.0000000
## [31] 0.0000000 0.0000000 27.9807047 24.9720297 20.9784381 17.9848739
## [37] 15.9848411 13.9761831 10.9782943 7.9696127 3.9847807 1.9847760
## [43] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 30.9808025
## [49] 27.9807612 24.9742932 20.9871050 18.9784702 15.9870641 13.9870225
## [55] 11.9718774 7.9804583 4.9848170 2.9847984 0.9913441 0.0000000
## [61] 0.0000000 0.0000000 0.0000000 0.0000000 31.9894746 29.9894241
## [67] 27.9744186 23.9829388 20.9871472 18.9871057 16.9784881 13.9870647
## [73] 11.9805418 8.9783769 5.9783583 2.9869546 0.9934635 0.0000000
## [79] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 32.9917348
## [85] 30.9894945 28.9831011 25.9852143 22.9893714 20.9807770 17.9893126
## [91] 15.9892624 13.9870928 11.9805979 8.9805567 5.9869965 3.9848711
## [97] 1.9848662 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [103] 0.0000000 35.9918369 33.9895872 31.9895508 29.9895144 27.9831210
## [109] 24.9830709 21.9894053 19.9893550 17.9871760 15.9871484 13.9871209
## [115] 11.9806401 8.9870522 6.9784590 3.9934918 2.9848888 0.9914059
## [121] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 37.9856198
## [127] 34.9896434 32.9896070 30.9895707 28.9958496 27.9809713 24.9809300
## [133] 21.9872591 19.9872316 17.9872041 15.9871766 13.9871491 11.9806823
## [139] 8.9870940 6.9870529 4.9849574 2.9870115 0.9934920 0.0000000
## [145] 0.0000000 0.0000000 0.0000000 0.0000000 39.9834898 36.9834397
## [151] 33.9896633 31.9896269 29.9895905 27.9958692 26.9831889 23.9831388
## [157] 20.9894450 18.9894086 16.9957425 15.9872047 13.9871772 11.9807245
## [163] 8.9871221 6.9870946 4.9870671 2.9870396 0.9935060 0.0000000
## [169] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 39.9920216
## [175] 37.9919625 35.9834736 32.9896832 30.9896468 28.9958839 27.9874117
## [181] 25.9832229 22.9831727 19.9957936 18.9872879 16.9872739 14.9957258
## [187] 13.9872053 11.9807667 8.9871503 6.9871228 4.9870952 2.9870677
## [193] 0.9935201 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## [199] 0.0000000 36.9897758 34.9835076 31.9897031 29.9896667 27.9959035
## [205] 26.9895939 24.9895439 22.9810566 19.9873571 17.9894484 15.9957543
## [211] 14.9872744 12.9957091 11.9808089 8.9871784 6.9871509 4.9871234
## [217] 2.9935346 1.9850289 0.0000000 0.0000000 0.0000000 0.0000000
## [223] 0.0000000 0.0000000 33.9835415 30.9959409 29.9875093 21.9895275
## [229] 19.9873717 17.9873441 15.9873300 13.9957376 12.9872749 10.9893094
## [235] 8.9872065 6.9871790 4.9871515 2.9935620 1.9870964 0.0000000
## [241] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 18.9895245
## [247] 16.9957886 15.9873447 13.9873305 11.9893790 9.9893426 7.9893062
## [253] 5.9956531 4.9871796 2.9935760 1.9871246 0.0000000 0.0000000
## [259] 0.0000000 0.0000000 0.0000000 0.0000000 16.9874137 14.9957719
## [265] 13.9873453 11.9873178 9.9809486 6.9956816 5.9936176 4.9872077
## [271] 2.9935901 1.9871527 0.0000000 14.9874141 12.9957552 11.9810320
## [277] 8.9893692 6.9936454 5.9872764 3.9956423 2.9936042 1.9871808
## [283] 10.9894255 8.9873465 6.9873320 4.9956707 3.9936320 7.9894220
## [289] 5.9956992 4.9936598 5.9873880Average Raster value by Vector shape
Let’s get each tract’s average elevation
mean_elev = lapply(elev, mean, na.rm = T)
head(mean_elev)## [[1]]
## [1] 59.591
##
## [[2]]
## [1] 58.46084
##
## [[3]]
## [1] 59.6559
##
## [[4]]
## [1] 60
##
## [[5]]
## [1] 60
##
## [[6]]
## [1] 60mean_elev[100]## [[1]]
## [1] 11.38207# Compare that to
mean(elev[100])## Warning in mean.default(elev[100]): argument is not numeric or logical:
## returning NA## [1] NA#oops - use unlist to flatten a list of vectors to a single vector
mean(unlist(elev[100]))## [1] 11.38207Add elevation to Vector object
Let’s add this to the SFtracts_NAD83 data.frame.
Note: Since the order remains the same, we can just add this right in!
SFtracts_NAD83$mean_elev = unlist(mean_elev)
head(SFtracts_NAD83)## Simple feature collection with 6 features and 11 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -122.4432 ymin: 37.77376 xmax: -122.4055 ymax: 37.80218
## Geodetic CRS: NAD83
## STATEFP COUNTYFP TRACTCE AFFGEOID GEOID NAME LSAD ALAND
## 1 06 075 010700 1400000US06075010700 06075010700 107 CT 183170
## 2 06 075 012201 1400000US06075012201 06075012201 122.01 CT 92048
## 3 06 075 013102 1400000US06075013102 06075013102 131.02 CT 237886
## 4 06 075 013500 1400000US06075013500 06075013500 135 CT 235184
## 5 06 075 015500 1400000US06075015500 06075015500 155 CT 311339
## 6 06 075 016300 1400000US06075016300 06075016300 163 CT 245867
## AWATER pop14 geometry mean_elev
## 1 0 5311 MULTIPOLYGON (((-122.4129 3... 59.59100
## 2 0 4576 MULTIPOLYGON (((-122.4183 3... 58.46084
## 3 0 2692 MULTIPOLYGON (((-122.4302 3... 59.65590
## 4 0 2592 MULTIPOLYGON (((-122.4362 3... 60.00000
## 5 0 3918 MULTIPOLYGON (((-122.4432 3... 60.00000
## 6 0 4748 MULTIPOLYGON (((-122.4332 3... 60.00000Map it
#what did we get?
elev_map <- tm_shape(SFtracts_NAD83) +
tm_polygons(col = 'mean_elev') +
tm_layout("The pain of biking in SF, by census tract",
inner.margins = c(0, 0, 0.1, 0),
title.size = 4.8)
#display map
elev_mapMap it
One step Re-do
We can also pass a function argument to raster::extract
elev <- extract(DEM_NAD83_crop, SFtracts_NAD83, fun=mean)
#what did that give us?
head(elev)## [,1]
## [1,] 59.59100
## [2,] 58.46084
## [3,] 59.65590
## [4,] 60.00000
## [5,] 60.00000
## [6,] 60.00000Questions?
Do you see the difference between those two approaches?
Mapping a vector layer on top of a raster layer (i.e.
my_map)Summarizing raster values by vector polygons, then mapping the polygons (
elev_map)
Challenge 2: Read in and check out new data
You have another raster dataset in your ./data directory. The file is called nlcd2011_sf.tif.
This is data from the National Land Cover Database (NLCD).
It’s 2011 data that was downloaded from here.
Read that file in as an object called nlcd, and plot it.
Solution
# read in nlcd data
# plot nlcdTake a look at the raster metadata
nlcd <- raster(here("notebook_data",
"part_3",
"nlcd2011_sf.tif"))
nlcd## class : RasterLayer
## dimensions : 609, 656, 399504 (nrow, ncol, ncell)
## resolution : 30, 30 (x, y)
## extent : -2287455, -2267775, 1946115, 1964385 (xmin, xmax, ymin, ymax)
## crs : +proj=aea +lat_0=23 +lon_0=-96 +lat_1=29.5 +lat_2=45.5 +x_0=0 +y_0=0 +datum=NAD83 +units=m +no_defs
## source : nlcd2011_sf.tif
## names : nlcd2011_sf
## values : 0, 255 (min, max)Let’s see what’s in the NLCD data
freq(nlcd)## value count
## [1,] 11 222187
## [2,] 21 21713
## [3,] 22 19966
## [4,] 23 61919
## [5,] 24 54480
## [6,] 31 1150
## [7,] 41 294
## [8,] 42 3406
## [9,] 43 4744
## [10,] 52 7224
## [11,] 71 2109
## [12,] 90 267
## [13,] 95 45… and a barplot
(Note: The colors in this barplot have no relation to the colors in our maps! Just pay attention to the categories on the x-axis.)
barplot(nlcd)
What do those values mean?
This is a categorical raster. Each cell on the raster holds a discrete (integer) value, coding a particular type of land-cover (rather than a continuous value, like we saw with our elevation data above).
Where do we do to figure out what the codes mean? This should come with the metadarad that ships with your data, or that is provided at the website where you downloaded it.
Here’s the NLCD legend.
Challenge 3: Reproject and crop our NLCD data
Now that we’ve read in our NCLD data, check if we need to reproject it (we want it to be in the same projection as our SFtracts object), and project it if need be.
Then crop it to the extent of our SFtracts object.
Your Solution
# check projection equality
st_crs(nlcd) == st_crs(SFtracts_WGS84)## [1] FALSE#reproject
nlcd_WGS84 = projectRaster(nlcd,
projectExtent(nlcd, st_crs(SFtracts_WGS84)$proj4string))
#check projection equality again
st_crs(nlcd_WGS84) == st_crs(SFtracts_WGS84)## [1] TRUE#crop
nlcd_WGS84_crop = crop(nlcd_WGS84, SFtracts_WGS84)Plot the new raster
plot(nlcd_WGS84_crop)
Recovering our plot formatting
Notice that the colors of our original, which conveniently represented the NLCD class colors from their website, are lost after reprojecting and cropping our raster.
Those colors were controlled by information in the original file, which was read into the @legend slot. Here’s the info (with hexadecimal format for color codes, e.g. ‘#00F900’):
nlcd@legend## An object of class ".RasterLegend"
## Slot "type":
## character(0)
##
## Slot "values":
## logical(0)
##
## Slot "color":
## logical(0)
##
## Slot "names":
## logical(0)
##
## Slot "colortable":
## [1] "#000000" "#00F900" "#000000" "#000000" "#000000" "#000000" "#000000"
## [8] "#000000" "#000000" "#000000" "#000000" "#476BA0" "#D1DDF9" "#000000"
## [15] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [22] "#DDC9C9" "#D89382" "#ED0000" "#AA0000" "#000000" "#000000" "#000000"
## [29] "#000000" "#000000" "#000000" "#B2ADA3" "#F9F9F9" "#000000" "#000000"
## [36] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#68AA63"
## [43] "#1C6330" "#B5C98E" "#000000" "#000000" "#000000" "#000000" "#000000"
## [50] "#000000" "#000000" "#A58C30" "#CCBA7C" "#000000" "#000000" "#000000"
## [57] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [64] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [71] "#000000" "#E2E2C1" "#C9C977" "#99C147" "#77AD93" "#000000" "#000000"
## [78] "#000000" "#000000" "#000000" "#000000" "#DBD83D" "#AA7028" "#000000"
## [85] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#BAD8EA"
## [92] "#B5D3E5" "#B5D3E5" "#B5D3E5" "#B5D3E5" "#70A3BA" "#000000" "#000000"
## [99] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [106] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [113] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [120] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [127] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [134] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [141] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [148] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [155] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [162] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [169] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [176] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [183] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [190] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [197] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [204] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [211] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [218] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [225] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [232] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [239] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [246] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [253] "#000000" "#000000" "#000000" "#000000"Recover our plot formatting
What’s the @legend slot in our reproject, cropped object look like?
nlcd_WGS84_crop@legend## An object of class ".RasterLegend"
## Slot "type":
## character(0)
##
## Slot "values":
## logical(0)
##
## Slot "color":
## logical(0)
##
## Slot "names":
## logical(0)
##
## Slot "colortable":
## logical(0)Recover our plot formatting
Well that’s a bummer…
Is there a way we could transfer that information over to our reprojected, cropped raster?
Transferring our @legend info
Without looking ahead, think about how to transfer the @legend info from the original raster object to our new object.
Solution
nlcd_WGS84_crop@legend = nlcd@legend
plot(nlcd_WGS84_crop)
Aaalllmoost…
Looking good!
But what are all those funky-colored speckles?
Turns out that raster reprojection requires interpolation of values, in order to bring one grid’s values to another, unaligned grid’s values.
By default, raster uses bilinear interpolation to do this. But this doesn’t make sense for categorical variables, because it returns non-sensical fractional categorical values!
We can change this behavior by telling raster::projectRaster to use nearest-neighbor interpolation instead.
The ?projectRasterdocumentation notes that this method is better suited to categorical data.
So let’s do that:
#reproject again, this time using nearest-neighbor interpolation
nlcd_WGS84 <- projectRaster(nlcd,
projectExtent(nlcd,
st_crs(SFtracts_WGS84)$proj4string),
method = 'ngb') # Nearest neighbor
#check projection equality again
st_crs(nlcd_WGS84) == st_crs(SFtracts_WGS84)## [1] TRUE#crop again
nlcd_WGS84_crop = crop(nlcd_WGS84, SFtracts_WGS84)
#grab our legend again
nlcd_WGS84_crop@legend = nlcd@legend
#plot to check again - dan, dan, dah!
plot(nlcd_WGS84_crop)
Selecting Cells with Specific values
# Take a look at just the nlcd cells coded developed, low density (22)
lowdens <- mask(nlcd, nlcd == 22, maskvalue=F)
freq(lowdens)## value count
## [1,] 22 19966
## [2,] NA 379538plot(lowdens)
Changing Raster Values
# Recode the values to 1
lowdens1 <- lowdens
lowdens1[lowdens == 22] <- 1
freq(lowdens1)## value count
## [1,] 1 19966
## [2,] NA 379538plot(lowdens1)
Raster Math - Map Algebra
We can add, subtract, mult, divide, etc, raster of the same extent (CRS) and resolution.
Here is just a dummy example!
lowdens2 <- lowdens1 + lowdens1
freq(lowdens2)## value count
## [1,] 2 19966
## [2,] NA 379538Reclassifying rasters
When we’re working with a categorical raster we’ll often want to reclassify our data. We may want to do this because:
- Our original data has more classifications than we actually need for our analysis.
- We want to represent the classifications we do have by a different numerical scheme because it somehow makes our analysis more convenient.
Reclass the NLCD
Let’s reclass our NLCD data. First we’ll need to define a reclassification matrix with 3 columns (low, high, to):
?reclassifyDefine reclassification matrix
See https://www.mrlc.gov/data/legends/national-land-cover-database-2011-nlcd2011-legend
#freq(nlcd) #to see all vals
# Note: by default, the ranges dont include left val, but include right
reclass_vec <- c(0, 20, NA, # water will be set to NA (i.e. 'left out' of our analysis)
20, 21, 1, # we'll treat developed open space as greenspace,
# based on the NLCD description
21, 30, 0, # developed and hardscape will be set to 0s
30, 31, NA,
31, Inf, 1) # greenspace will have 1s
# take a look at the table
reclass_vec ## [1] 0 20 NA 20 21 1 21 30 0 30 31 NA 31 Inf 1# Create the reclass matrix
reclass_m <- matrix(reclass_vec, ncol = 3, byrow = TRUE)
reclass_m## [,1] [,2] [,3]
## [1,] 0 20 NA
## [2,] 20 21 1
## [3,] 21 30 0
## [4,] 30 31 NA
## [5,] 31 Inf 1Reclassify the raster
nlcd_green <- reclassify(nlcd_WGS84_crop, reclass_m)Reclassify the raster
What did we get?
freq(nlcd_green)## value count
## [1,] 0 74979
## [2,] 1 16578
## [3,] NA 114049Reclassify the raster
What did we get?
barplot(nlcd_green)
Reclassify the raster
What did we get?
plot(nlcd_green)
Challenge 4: Extract reclassed NLCD data to our tract polygons
Just like we did earlier with our elevation data, let’s extract our reclassed NLCD data to our census-tract polygons.
Solution
# extract the mean nlcd_simple values to tract polygons
#greenspace <- ...What did we get?
greenspaceWhy?
What’s with all the NAs?
Remember, we set all water cells to NA, to ignore them in our analysis.
How do we get extract to ignore our NAs?
Let’s run the same command again, but telling the extract function to ignore NAs.
The na.rm argument will do this for us. See how the docs indicate that it is set to FALSE by default?
?raster::extractGood to know! Also good to know that this is a common argument across a variety of R operations.
Removing NAs in Calculations
#extract the mean nlcd_simple values to tract polygons,
#this time setting na.rm to TRUE
greenspace <- extract(nlcd_green, SFtracts_WGS84, fun=mean, na.rm = T)
#and add to our SFtracts dataframe (which we can do because order is preserved)
SFtracts_WGS84$prop_greenspace = greenspaceGet the mean home values in each tract
Pulling code from the end of Part II of this workshop, let’s aggregate our homes data to the tract level too.
#aggregate totvalue to SFtracts
SFtracts_w_mean_val <- aggregate(x = SFhomes15_WGS84['totvalue'],
by = SFtracts_WGS84,
FUN = mean)
#and add the totvalue column to our SFtracts dataframe
SFtracts_WGS84$mean_totvalue <- SFtracts_w_mean_val$totvalueGet the mean home values in each tract
Here we use the “quick tmap” function qtm.
qtm(SFtracts_w_mean_val, fill = 'totvalue')Predicting home values
Do mean elevation and proportion greenspace predict mean home values?
(Note: This is not a statistically valid model! Just an example of a raster data analysis workflow.)
mod <- lm(mean_totvalue ~ unlist(mean_elev) + prop_greenspace, data = SFtracts_WGS84)
summary(mod)##
## Call:
## lm(formula = mean_totvalue ~ unlist(mean_elev) + prop_greenspace,
## data = SFtracts_WGS84)
##
## Residuals:
## Min 1Q Median 3Q Max
## -712033 -309403 9402 248431 1761021
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1166105.7 61307.9 19.020 <2e-16 ***
## unlist(mean_elev) 1341.0 842.7 1.591 0.113
## prop_greenspace -146481.5 250481.8 -0.585 0.559
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 378100 on 184 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.01402, Adjusted R-squared: 0.003302
## F-statistic: 1.308 on 2 and 184 DF, p-value: 0.2728Predicting home values
Not at the census-tract level. But that’s kind of coarse…
What if we want to do the analysis at the property level?
We have added this workflow as an appendix in a separate document, 10_Raster_appendix.Rmd. It puts together a bunch of what we’ve learned over Parts I to III of the workshop. Feel free to give it try later!
Questions?
Section 3: RasterStacks and RasterBricks
RasterStacks
A RasterStack is a collection of RasterLayer objects with the same spatial extent and resolution.
A RasterStack can be created from RasterLayer objects, or from multiple raster files.
#?raster::stack
# Create a stack from 2 rasters
DEMx2 <- stack(DEM_NAD83_crop, DEM_NAD83_crop_masked)
DEMx2## class : RasterStack
## dimensions : 187, 224, 41888, 2 (nrow, ncol, ncell, nlayers)
## resolution : 0.0008333663, 0.0008333239 (x, y)
## extent : -122.5148, -122.3281, 37.70781, 37.86364 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=NAD83 +no_defs
## names : san_francisco.e.1, san_francisco.e.2
## min values : 0, 0
## max values : 303.9921, 269.8798# Plot the stack
plot(DEMx2)
# Plot one layer in the stack
plot(DEMx2[[1]])
# Does this work?
#demNelev <- stack(DEM_NAD83_crop, nlcd_WGS84_crop)RasterBrick
A RasterBrick is a multi-layer raster object that is created from a single file or raster stack.
Raster computations on a brick are faster than on a raster stack!
#?raster::brick
# Creating a brick from a stack
DEMx2brick <- brick(DEMx2)
# or
#DEMx2brick <- brick(DEM_NAD83_crop, DEM_NAD83_crop_masked)
#Take a look
DEMx2brick## class : RasterBrick
## dimensions : 187, 224, 41888, 2 (nrow, ncol, ncell, nlayers)
## resolution : 0.0008333663, 0.0008333239 (x, y)
## extent : -122.5148, -122.3281, 37.70781, 37.86364 (xmin, xmax, ymin, ymax)
## crs : +proj=longlat +datum=NAD83 +no_defs
## source : memory
## names : san_francisco.e.1, san_francisco.e.2
## min values : 0, 0
## max values : 303.9921, 269.8798# Summary stats
summary(DEMx2brick)## san_francisco.e.1 san_francisco.e.2
## Min. 0.0000 0.00000
## 1st Qu. 0.0000 30.01013
## Median 0.0000 60.00000
## 3rd Qu. 60.0000 69.99589
## Max. 303.9921 269.87975
## NA's 0.0000 23283.00000# Plotting
plot(DEMx2brick)
plot(DEMx2brick[[1]])
Raster Algebra
Calculations across raster layers
# Mean values
mean_dem <- mean(DEMx2brick)
hist(mean_dem)
Raster Algebra - thought exercise.
Where to start my SF apartment hunting?
My evaluative criteria?
- Land cover class is low-med intensity
- Elevation is high, I want a view
Approach? Let’s discuss
# Psuedo code as commentsQuestions?
Additional Resources
Geocomputation in R - THE book on working with geospatial data in R. Raster sections feature the new+fabulous
terrapackage.A National Center for Ecological Analysis and Synthesis tutorial
A really well organized, intro raster tutorial by Dr. Emily Burchfield